An the issue is only inside the network? I’d complain to IT about that, yeah. Maybe they are overriding the DNS record with their own DNS server or something.
Can you set your own DNS servers on your client devices? Does cloudflare or quad9 resolve it?
Sure, the docs are pretty minimal though: https://wiki.servarr.com/prowlarr/settings (just click on Proxy)
Basically you can configure a proxy (from your VPN provider for example) for each indexer (or font add a tag to apply it to all of them), and queries to indexers will run through there. This avoids Sonarr making calls to TVDB or whatever through the VPN and getting blocked.