They went through the full multi-round set of testing that all vaccines go through in the US (even ignoring the overlap elsewhere), and have since been administered to hundreds of millions of people. I'd call that well tested, yes.

What would be the point of me pretending it's up for debate? I'm not stopping you from sharing whatever concerns you have, not sure how you think I even would. I'm not likely to be interested in them if I'm being honest, I've seen far too many sites and stories already. But you do you.