Final Cut Pro

The only version available from the App Store is the current version. To buy the application you will have to do that once a system that can run it, a computer with 11.5.10 or later. Once you've purchased the application using your Apple ID, you can then download the version appropriate for your 10.12.6 system form the Purchased page of the App Store, not from the main FCP page.

I am not sure exactly what version would run in such an old OS - maybe 10.4, or so.

You can't just buy an old version, but if you already have bought FCP, you can download a version compatible with your OS.

So, first: do you already have Final Cut Pro?

If you do, all you have to do is go to the App Store, logged in with your Apple Id, click on Purchased and then click the Download link next to FCP.

If you need to buy first - and you are sure, as this is not just small change, to use on an old machine - then what you can do is use some mac running at least Big Sur 11.5, log in to the App Store with YOUR Apple Id, make the purchase and delete the application; then back at your older mac, proceed as described above.

But in the latter case, do consider if another option may better for you. Perhaps iMovie (free) can do what you need.