'Connect' page similar to Sonarr/Radarr
Be able to set up custom postprocessing hooks.
Even if you don't support all the built in options that they do, just being able to use a custom script with triggers like 'on subtitle download' and 'on subtitle update/delete' would be perfect.
For my use case It would tell my media library software (jellyfin/plex/emby) to rescan the library. Depending on the nuances of one's system, features built into the media library software like continuous file system monitoring might not work/may be undesirable. So either something has to use an API to trigger the refresh or it just waits for schedules scans. But with 'connect' I can just call a script that inerfaces with the Jellyfin API. I think this is a key feature of Sonarr/Radarr that Bazarr is missing.