I am on Finale 25 - if I upgrade Safari, will my curent OS (High Sierra) automatically upgrade to the

next OS - and - will my current pending Finale files open to the new OS. For my purposes, I have

no need to to upgrade Finale - but if I have to, will the next level of Finale open my current files

Unless it specifically includes an OS upgrade, (which I completely doubt,) upgrading Safari will have absolutely no affect on Finale.

1) No. You can upgrade Safari only (System Preferences -> Updates) without upgrading macOS.

2) All your current files can be opened by all versions starting with Finale 2014 (25,26,27).

What Mac do you have?

OS 10.13.6....High Sierra

That wasn't my question. This was:

What Mac do you have?

27"  I Mac

I think Mike H wants to know the year. It’s on the About This Mac screen. The reason it’s important is that the 2017 iMac (or earlier) maxes out at Ventura, and can’t be upgraded to Sonoma.

and a 2010 maxes out at High Sierra and so on…

"Late" 2015

You can go to Catalina, according to https://www.google.com/search?q=latest+mac+os+for+late+2015+imac&ie=UTF-8&oe=UTF-8&hl=en-us&client=safari

A 2015 iMac can go until Monterey (MacOs 12).

https://www.macworld.com/article/673697/what-version-of-macos-can-my-mac-run.html 

If you want to stick to Finale 25, Mojave (10.14) is the limit, according to MakeMusic.

https://makemusic.zendesk.com/hc/en-us/articles/216545087-Finale-Notation-Software-System-Requirements

If you upgrade to a more recent system (for your 2015 iMac, MacOs 12 Monterey is the limit), you will be forced to get Finale 27.

https://support.apple.com/en-am/103260