The longest delay of any suspected side effect from other vaccines is about 6 weeks, and this represents the extreme limit of attributable causes for Guillan-Barré syndrome. Although the potential complications of an adverse vaccine reaction can endure for a long time, we simply don't see new side effects appearing out of the blue months or years later. This is different from medications, which people take continuously and from which chronic toxicities can and do develop. But there really isn't a plausible biologic mechanism how vaccine material, which lingers in the body only very briefly before being broken down, metabolized and excreted, could cause some chain reaction of events that only present much later. Close to a century of safety observation in other vaccines confirms this.
Out of 10s of millions of doses given worldwide thus far, there has not been a single case of Guillan-Barré temporally associated with vaccination (although it should be noted that plenty of people still remain within the potential time window). The worst known reaction thus far is anaphylaxis, which is easily treated and has thus far not resulted in a single death or prolonged hospital stay. Both of the trials of the current mRNA vaccines reported some cases of Bell's palsy, but at a frequency below that of the background population rate. The overall picture from these vaccines is that they are incredibly safe.
Finally, we (in the medical field) knew about the Kawasaki-like syndrome that some kids with COVID-19 can develop back in April. It probably just wasn't publicized in the lay press until much later.