Totally right.
Absolutely all human medicine is experimental in the same way the person is using "experimental vaccine". Anything else would not be science.
The only question is usually how many experiments have been run and on who and what do we extrapolate from them.
But make no mistake - nothing could possibly be proven safe to a given person without having been tested on that person. You are unique. This is precisely why this is not the standard used for safety, and can't be.
Maybe some century we will have that capability, but it does not exist right now.
If you go buy an orange from the grocery store, that's experimental in the same way - i guarantee you it's mutated at least a little from the other oranges you've eaten. How can you be sure the mutations will not have a harmful effect?
(This isn't even a joke - mutation is quite common in citrus, and thing like the cara cara came from natural orange tree mutations)
As far as testing goes - in the history of vaccines that were deployed quickly (polio, smallpox, etc), the covid vaccines are very well tested.
The space of things we don't continuously test and track for safety is basically infinite, and the likelihood of harm coming from that infinite space of untested things is much greater (overall) than "a thing we've given to hundreds of millions of people and explicitly kept track of the side effects"
This is proven to be true again and again - eventually we notice the effect of things we weren't looking at, take some of them, test them, and say "well crap, actually, this is really harmful".
Meanwhile, outside of intentional fraud/malice, it's much more rare that the things we are testing and tracking continuously on large groups of people turn out that way. When they do, it's often because of long term effects you couldn't discover without time anyway.