I haven’t been keeping up, what Thunderbolts run did they base the new movie on?

None of them, as far as I can tell. It wouldn’t bother me, except that we haven’t seen Screaming Mimi or Songbird in the MCU yet, and I’m concerned they’ve decided not to include her because her powers are expensive to CGI.

I’m worried that there’s not many Thunderbolts stories that work without Songbird.

It would make sense to try to fit Yelena into that role, but I’m not sure that will resonate the same way. Screaming Mimi wasn’t a villain due to a global secret conspiracy. She just liked money.