After any reboot of macOS Sequoia (15.0) the Emby app will fail to play media from an emby server on the same LAN until the Settings > Privacy & Security > Local Network > Emby setting is toggled off and on again (despite being set to on to start with). In other words, this Local Network access permission seems to be forgotten on each reboot (even though the macOS UI shows it as turned on) and toggling this off and on again reapplies the permission so the Emby app can work as usual.