I won't comment on vaccines not approved in the US, because I have not followed them closely, but because you bring it up...
There have been zero deaths associated directly with the mRNA vaccines, both in the clinical trials, and after several hundred million doses administered across the world. The expected minor and brief illness symptoms after the second dose are so widely known and documented on this website that I wouldn't even have thought it was worth mentioning. The most serious side effects associated with these vaccines has been anaphylaxis, at a frequency of between 2 to 5 per million doses. Most were able to be treated on the spot with an epinepherine injection, and a small minority required overnight observation in a hospital. There were no deaths associated with anaphylaxis. There have been no reported associations with some of the more serious reactions seen with pre-existing vaccines, such as Bell's palsy, transverse myelitis, thrombosis or Guillan-Barre syndrome.
For the Johnson & Johnson vaccines, besides the usual injection site reactions, there is a very small, but real risk of thrombosis, about 3 per million in the general population, but as high as 12 per million in women of reproductive age. I don't have the exact numbers, but I think there were at least two deaths associated with cerebral venous thrombosis, and although the condition was likely triggered by the vaccine, the deaths themselves were caused by using the wrong treatment (heparin).
So, nobody ever claimed these vaccines were completely without side effects (few vaccines are), but other than some very rare adverse reactions, the vaccines are extremely safe, particularly the mRNA vaccines. And the numbers affected are several orders of magnitude less than what we have seen from COVID, both in deaths and in long-term morbidity, the latter of which does not closely correlate to underlying health conditions.
Finally, and this has been stated again and again on this website, but because you brought it up, I'll state it again. The "we don't know the long-term side effects of the vaccines" is a canard. Out of every vaccine previously developed, the longest latency we've seen for the appearance of a side effect that can be reasonably tied to a vaccine is about 6 weeks. This represents the outer limit to how long Guillan-Barre syndrome might appear following influenza or meningococcus vaccination, and the risk of this reaction is about 1 per million or less. There really isn't a feasible biochemical mechanism for a vaccine to suddenly trigger a reaction months or years later. If a vaccine does trigger an auto-immune reaction, this occurs within days to weeks, not months to years. We now have over a year of trial data on the COVID vaccines, and 6 months of real-world experience, plus over a century of vaccine research in general "Long-term side effects", unless they're part of the sequelae of an acute reaction, really aren't something that exists with vaccines.
