I don't think it's very useful to maintain this list by hand.

It's a duplication of information, and such things always

invariably end up outdated and useless.

I think it's more useful to write a program that collects

this information automatically. The fact that you're

finding this task boring and repetitive is enough of a hint

that such a program can be written. I'd say start with

a dolist of known major modes and a temp buffer,

set the buffer in the major mode and check if there's

a buffer-local value of flymake-diagnostic-backends.

Also, given the advent of LSP, I think the trend is

for Flymake to be chiefly useful when connected

with something like Eglot. Not exclusively so, but

rather predominantly so.

João