We currently have an open R&D ticket for the issue where audio devices disappear during startup on the latest macOS (Tahoe). As mentioned by @Jin-Bin_Yang, there’s no need to log out — simply restarting the Roon Server should temporarily resolve the issue.
We’re sorry for the inconvenience, and we expect this to be fixed in an upcoming release.
The issue you’re describing is limited to MacOS Sequoia, and in most cases only the releases preceding MacOS 15.6.
Sequoia tends to mistake Roon updates for new software, removing them from the Local Network permissions list. You simply need to toggle Local Network access back on for Roon in Privacy & Security → Local Network.