Postgres backups are tricky for sure. Even if you have a DR plan you should assume your incremental backups are no good and you need to restore the whole thing from scratch. That’s your real DR SLA.
If things go truly south, just hope you have a read replica you can use as your new master. Most SLAs are not written with 72h+ of downtime. Have you tried the nuclear recovery plan, from scratch? Does it work?