Why is my high speed Screen Sharing not working on my Mac running macOS Sonoma?

This week, after many months of being able to use my MacBook Pro (M1, Sonoma 14.7.2) via High Performance Screen Sharing on my Mac Studio (M2 Max, Sonoma 14.7.5), it no longer works right.

First, when I try to connect, the Screen Sharing connection rejects my saved password. It brings up a dialog to use passwords from the keychain, but I just hit cancel and then it accepts my saved password. That's strange, but not the worst thing.

The worst thing: I make connection, and ... I can move the mouse, but clicking does nothing... nothing visible. Since the laptop screen is dark, I cannot see what is happening on the laptop, but after I break the connection, it does appear that my clicks took effect. However, I did not see the effects of clicks on the screen as displayed on my Mac Studio.

This problem seems to be limited to High Performance connections. The laptop is plugged in to the network with an ethernet adaptor, and in the past, this connection has been fine and perfect.

Odd, no?

[Re-Titled by Moderator]

Original Title: Screen Sharing High Speed No Longer Works: cannot click