I can see the screen but the pointer does not move

Seeing and controlling are two separate permissions on a Mac, and this is the commonest confusion there is. Screen recording covers watching only; for somebody to move the mouse and type, the same application additionally needs accessibility. Granting control inside the meeting application changes nothing here — that asks the other side, it does not grant the system permission.

Accessibility — Lets the application move the mouse and type. Without it somebody can watch, but touch nothing.

If remote control stays grey inside the meeting application, the Mac may not be the problem at all: Zoom can switch it off account-wide in its web portal, and Microsoft Teams disables handing over control by itself while macOS content sharing is enabled in the Teams settings.