This encapsulates a misunderstanding of how vaccines work. They do not float around in our bodies for years. They work by (hopefully) training an immune response from our own bodies. The vaccines themselves rapidly breakdown. They do not last because there's no need for them to. As a result, vaccine testing - for all vaccines - pretty much only needs to cover that period. While side-effects (ranging from minor to serious and rare to common) from the vaccines themselves do occur, what's not clear to me is how well we understand/appreciate the second order effects of an altered immune system response e.g. "my body now knows to attack X, but in attacking X, it also impacts Y" - kind of thing. Where Y may be something that only becomes apparent much later.

Speaking for myself, having lived and worked in SE Asia for a while, I've had almost every vaccine known to man (the only one I'm sure I haven't had is the HPV). I've had 5 COVID shots (got COVID once in 2021) and get an annual flu-shot. The only side-effect I've ever had (that I'm aware of), is a sore arm at the injection site. I have no idea what that says about me. My mum reacts badly to most (not all) vaccines - especially the flu shots. People vary and I suspect our immune system (which I believe is poorly understood) has complex effects on the response to some vaccines.