Screen Sharing Locks Keyboard and Mouse on Host Mac in macOS Sequoia

Every single time I use screen sharing in macOS Sequoia to connect an M3 MBP (Max) to a remote M1 MBP (Max) on my home LAN the mouse vanishes and the keyboard stops responding on the host as well as the remote. This happens after a few seconds or a few minutes. The machine is effectively frozen and only a power cycle gets me out of it. This is strictly a Sequoia issue through the latest release (15.1). I have tried disabling high performance mode and that doesn't help.