Hi Quinn,
I have exactly the same problem on macOS 15.1 and the latest 15.2.
Install the app, first time it accesses the local network the dialog appears. I grant permission and Local Network access works.
Reboot the machine, launch the app, now local network access fails.
Go into System Settings -> Privacy & Security -> Local Network and I can see my app as Local Network permission.
Toggle it off and back on, and local network access starts working again.
Happy to provide a copy of my app, it doesn't require a licence.
Regards
James Milne
FilmLight Ltd.
Topic:
App & System Services
SubTopic:
Networking