How to center an element independently from the container?

I have a container that looks like this:
container with links

(the text is in Georgian but that doesn’t matter)
problem is that the search field and it’s button are not centered, and I can’t fix it for a long time now.

I tried using z-index but that didn’t work, tried asking chatgpt too but it didn’t help either, it either messes up my code or doesn’t change anything at all.