Many admins who have tried, reported a local server does not appear on the LAN tab in the steam browser.
Connect using the console command.
If the port is 27015, then you can just use : connect IP
Add server to favourites
Add the server to the server browser's favourites. If in-game, then go to the legacy browser if applicable to find it. The syntax to use is the same as for the console connection.
Make sure your server actually works and is reachable on LAN, otherwise what you need is rather Troubleshooting first.
As this github issue shows, there might be a possible configuration that fixes the issue, but LinuxGSM devs were not able to reproduce it at the time of writing the doc, so this information is purely experimental and you are welcome to update it or post on the issue if you have useful information to share about it.