possible to save my search-replace

How about recording and saving a macro of it? A potential downside is that it becomes a “fixed” operation at that point, you can’t easily edit it to tweak it. You’d have to find it in shortcuts.xml to do that.

Far from ideal, but if you have a search-not-replace operation and you record it in the context of a Find all in current document macro, when you run it, it (the search expression) will appear in the Search "blah" (10 hits in 1 file) area and you can easily then copy the blah part out and tweak it for a subsequent search. I find this useful sometimes in the context of a complicated regular expression search.

@PeterJones

save the last 10 or so expressions,

Yes but as they are not saved as pairs it is easy to lose track of which search term goes with which replace. And you can’t give it a mnemonic name like you can with a macro.

Do you need more than that?