Sounds like you got bit by what I did when I upgraded my Mac from a 2011 mini running Sierra to a 2018 mini running Catalina. Starting with macOS 10.15 (Catalina), support for 32-bit apps was dropped - everything must be 64-bit.
FileMaker Pro switched from 32-bit to 64-bit with version 16, so all older versions stopped working after Catalina. In my case, it was version 11 that stopped working.
I paid the $594 for version 19 (two years ago), with the expectation that it will last long enough that the overall per-year cost won’t be too horrible. My guesstimate/hope is that it will work until Apple drops Rosetta from Apple Silicon macOS, at which point I’ll need to buy an ARM build of FM.
(You may want to skip the next two paragraphs, which explain the logic I’m hoping will prove to be true)
If you don’t want to bet on my assumption proving to be true, another option is to buy an older version that may cost less. There are some sellers on-line selling FMP 16 license keys for a much more reasonable price. Just be sure to do your homework and check out the seller’s reputation, since you don’t want to pay a scammer for a license key that is bogus, reused or counterfeit.
I see that Amazon is selling version 19 for $540. Still pricey, but a $54 discount isn’t insignificant either. Amazon.com
If you or someone in your household is a full-time student or works for a school or a non-profit organization, you may qualify for educational pricing. Claris Store. Amazon sells the educational edition for $324 (Amazon.com), but I don’t know what kind of proof may be required to install what you buy, or if you’re on your honor to not cheat. (Please don’t cheat - when people do that, companies get more draconian, making life more difficult for students who need these discounts.)
You could also install a 32-bit compatible version of macOS in a VM (10.14 “Mojave” or older) and run your existing copy of version 12 in it.