OK, so a lot of information to go over here, and to adequately explain things, we need to take kind of a deep dive into biochemistry and immunology. Like a lot of things in medicine, you can't give a quick answer without an understanding of some of the underlying concepts.
First of all, we need a solid definition of what constitutes a "protein" and what makes one protein different from another. Ask someone on the street, and to the question of "What is a protein?", they might reply "It's something we eat", which although true, is not a particularly useful answer. So, here we go... proteins are large biochemical molecules made up of long chains of amino acids. Almost every protein in every living organism is made of just 20 different amino acids. The genetic code (DNA and RNA) specifies the exact amino acid sequence in every protein. The primary sequence of the amino acids determines the how the chain folds over on itself, and this three dimensional folding is what gives each protein its unique chemical and physical properties. The average protein contains a chain of about 500 amino acids, so given 20 potential different building blocks that can be used for each link in the chain, the sheer raw number of possible unique configurations of just an average sized protein is an almost unfathomably large number. Kind of like a box of Legos contains a limited amount of different sized pieces, but there's an almost infinite number of ways they can be put together.
In addition to the primary sequence, the 3 dimensional shape, and therefore, the way a protein functions is influenced by its immediate environment: the temperature, the electrical charges of other molecules in the vicinity, the chemical composition of the environment, including the pH, concentrations gradients, etc. Every protein has a range of all of these parameters where it functions optimally. Take it outside those parameters, and the 3 dimensional folding will alter, thus stopping the protein from its primary function or even damaging it. Some proteins function in the unique environment inside particular cells, some on the surface, and a few, like antibodies, insulin, and clotting factors, to name just some examples, maintain their optimal configuration flowing through the blood.
In every organism with an immune system, all proteins contain a semi-unique residue of protein and carbohydrates that serves as a marker of "self", so that the surveillance systems of the immune system don't set off the alarms and attack that particular organism. In humans, this is known as the "human leukocyte antigen", or, HLA. Any protein (and some large non-protein molecules) that don't express that organisms particular HLA sequence sets off the alarms as "foreign", and generally gets picked up and degraded. Obviously, this system doesn't work perfectly, or we wouldn't have autoimmune diseases.
Now, to answer your question about the spike proteins in this study, and the spike proteins in the vaccine. Other than some minor but crucial amino acid changes amongst the variants, they are functionally the same. But is this relevant? Almost certainly not.
First of all, the study you posted was an in vitro study, which is relevant to the specific question the researchers were trying to answer, but much less relevant to the vaccines. What they found in the study was that the mere presence of the spike protein binding to the ACE receptors of the lung was sufficient to cause a short activation of the complement system, even without the viral genetic material being injected into the target cells. Complement in this context is a localized chemical response that cells give off when infected with a virus, that gets amplified by the surrounding cells and summons the specialized immune cells (macrophages, neutrophils, T lymphocytes) to the area. I think the key here is that the spike protein alone caused a relatively brief pro-inflammatory response. This was somewhat of an unexpected finding. In the context of an active infection, where the lung endothelium gets constantly bombarded with viral particles (and by extension, the spike proteins on the surface), this may be significant. If these results held in vivo, that would mean that spike proteins are effectively a "force multiplier" (in army-speak), because they add an additional factor that provokes more inflammation.
Now, back to proteins a bit, specifically the spike protein generated from the mRNA vaccines. The mRNA code is injected directly into the muscle tissue, where the lipid coating allows it to be inserted into the cytoplasm of the cells. This is where the mRNA uses the cells' own protein producing factories (ribosomes) to assemble individual amino acids into the correct chain sequence that makes the spike protein. The spike then gets exported to the cell surface, where, because it lacks the host HLA signal, sets off the immune cascade that brings in the macrophages. These large amoeba-like cells then "eat" the spike proteins, and while internalized, break them down into large fragments. These fragments, although they still contain sequences that are unique enough to be recognized as parts of the spike protein, are no longer functional. They have lost their unique 3-D configuration. Once the macrophages have traveled to the lymphocyte stem cells, they present these fragments to one stem cell at a time, until they find one that makes antibodies that can bind tightly to the spike protein fragments. This lucky cell then gets to multiply and forms the reserve army of B or T cells selected to recognize and attack the spike protein if it ever shows up again. At this point, the macrophage then completely degrades what is left of the spike protein fragments down into the raw amino acids, which can be recycled into something completely new. To use a Lego analogy, this would be like building a little Lego house, then breaking it down into large pieces. These fragments are still recognizable as parts of the house, although they no longer function by themselves as a house. And then, the house pieces are completely taken apart again down into the individual Lego bricks. Nothing remains that makes the pile of Lego bricks recognizable as the house they once formed.
OK, so where am I going with all of this...
1) To do the damage in the lungs, the intact, functioning spike protein actually needs to be in the lungs. The vaccine material is injected directly into the muscle tissue, with minimal penetration into the blood stream, and even here, whatever vaccine material enters the circulatory system only contains the instructions for the spike protein, not the spike protein itself.
2) Once the muscle cells express the spike protein, it gets pretty quickly gobbled up (as does any material the body recognizes as "foreign") by the afore-mentioned macrophages. Even if any spike protein did slip into the blood, the different chemical environment of the blood vs. the interstitial fluid that surrounds the muscle cells would change its configuration. And the immune surveillance system in the blood is about a million times more sensitive than outside the bloodstream. Anything recognized as foreign here gets almost immediately bound up and eliminated, unless there's just so much of it being continually produced that it overwhelms the immune response. So, I seriously doubt any significant amount of vaccine-induced spike protein will be able to migrate to the lungs. The half-life of the actual correctly configured spike protein from the vaccine is relatively brief in vivo. The enduring effect is not from the spike protein itself, but from the B and T cells that are recruited to recognize and fight it.
3) There is no evidence, after hundreds of millions of doses given, that people have suffered any lung damage from vaccination (barring perhaps some exceedingly rare allergic reactions).
4) Lung tissue actually recovers from injury quite well, unless you subject the lungs to almost constant bombardment from smoke, debris, or a raging infection. To give an example, even heavy smokers, who coat their lungs with multiple times daily with all kinds of harmful combustion residue, need to maintain their habit for years or even decades before we start seeing severe reductions in their pulmonary function testing. I can not possibly imagine that even if a tiny fraction of intact and functional vaccine-induced spike protein made it briefly to the lungs that it could do any lasting damage compared to the junk that most humans inhale (purposefully or by accident) on a daily basis.
(EDITED for clarity since my initial post)
Summary coming...
To be continued with a summary.