Here’s a paper about testing einstein’s theory:

https://arxiv.org/pdf/0806.1731

It is an older paper, but aftet a skim the only significant missing experiment is LIGO. At the scales which GR is fundamentally concerned we simply do not have sufficient data or technology to test.

If we had tested everything that could be for GR or it had no contraditions we wouldn’t be creating modified theories of gravity or proposing new constants to try solve things, or trying to come up with some quantum theory of gravity.

Hartle has a very simple way of viewing this, see photo from his textbook “Introduction to General Relativity”

One thing to remember is that GR is still just a theory with a substantial lack of experimental proof, but the maths does work out quite well with it.

I will believe it when I see it