Since I see no replies yet, I'll give a sort of answer. I use Overseerr and my own self hosted domain name with Cloudns so that I can let my friends/family connect to it remotely to request stuff.
It sounds like it's definitely not 1:1 with what you're asking for since it only does sonarr and radarr and is not something accessible from messengers, but figured I'd mention it because it's been great for me. I use it for myself to add new stuff as well so I never have to go into the individual sonarr/radarr instances to add stuff.
You might try SDTV or Fullscreen (plus DVD or VHS since those were the last formats that typically offered that aspect ratio regularly) as tags/search terms. I am otherwise unaware of any specific automated search options for 4:3 content. :/
Obviously it would take some work, but you could set up an automated set of scripts that would crop the videos and spit them out as 4:3.
Is there no option within the vr application itself to auto zoom and crop videos to fit the TV?