Disappearing Cursor

You get full screen mode when you click on the green "stoplight" button at the top of a window.

Use apps in full screen or Split View on Mac - Apple Support

You can also make the pointer one size larger, and/or enable: "shake mouse pointer to locate". I run with this enabled at all times.

Change Cursor preferences for accessibility on Mac - Apple Support.

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That computer uses Intel Iris 6200 Integrated graphics, and display memory is shared with System memory.

One reason that the cursor may disappear is if you invoke Full-Screen Mode. When you do the system seem to get confused about whether the cursor should be present and where.

Full screen mode is a feature reverse ported form the iPhone, land of tiny screens and one-at-a-time processing. In my opinion, you are almost always better off stretching the window to almost fill the display, rather than clicking the button for full-screen.

The other possibility os that your wireless mouse is not being seen. Bluetooth uses the same frequency band as 2.4GHz Wi-Fi, but does channel hopping to dodge your wi-fi traffic. It is subject to the same sorts of interference caused by badly-shielded USB-C and USB-3 peripherals.

There are more than a hundred computers that bear the name MacBook PrRo, from 2006 to the present day, and more than a dozen versions of MacOS they could be running.

¿which is yours?