I'm experiencing a similar issue.
Prowlarr is on a VPN network via Torguard/Wireguard
ARRs are on a custom network.
Prowlarr on the custom network talks fine, once it's on a VPN, I can go into APPs and test the connection. Logs read that they time out to each ARR container.
Looks to be about November 1 Prowlarr got corrupted somehow (logs were saying db corruption) so I just went through a fresh install (cleared file directory and everything). Prior to that everything was working fine while Prowlarr was on a VPN and the ARRs were on their own custom network. I know this doesn't assist you in solving the issue but I feel ya.