rdns dev here
LAN access generally has other problems when used with Rethink.
What Rethink version are you using? The latest on F-Droid is v055t. You can find the version information in the footer of the About UI.
Probably9857 Selecting System DNS in Rethink DNS config doesn't help. Nor does experimental setting for allowing LAN access (which seems like it is only relevant to the VPN feature, which I'm not using).
.local should be auto resolved by Rethink's built-in mDNS service provided Configure -> DNS -> Use System DNS for undelegated domains is turned ON.
What the Configure -> Network -> Do not route Private IPs does is exclude all RFC 1918 IPv4 addresses and ULA IPv6 address space from Rethink's tunnel. That may help if .local is resolved as expected by Rethink in the first place (which it should... but like you say it isn't).
If you are comfortable, you can look through what's going on when .local is recieved by Rethink by going to Configure -> Settings -> App logs.
- Use the search bar to filter for the
.local domain name you're trying to debug or generally use mdns: as the search term.
- Make sure to tap on the "filter" icon in the search bar to change the log level to "Very Verbose" (the default is "Error"). This log level will revert back to "Error" after ~3h or so (to conserve power use).
You can either copy paste the logs to ask any capable LLM chatbot (to help it, point it to this code) to see if it is able to help, or you can share them with me here or over on email (mz at celzero dot com). If you do email, please leave a link to this GrapheneOS discussion thread, so that it is easier for me to search through my inbox.