Redo flutter publish

[thomassth]

Part of #362

Referencing xvrh's work.

@nickrandolph also pointed out our json's formatting might have caused problems. Now we wrap it in a file properly so hopefully it works better now.

Also, their pipeline worked so I'm a bit more confident this time around 🤞

[sowens-csd]

So we don't need the publish action anymore because the flutter pub publish action will directly use the credentials?