You can first try to reinstall the Bluetooth drivers with the latest version available for your device model, from the manufacturer's website. The best and cleanest way to update a driver is to remove the drivers, first from Device Manager, and then reinstall the new drivers. To do so: Press Windows + X keys and select Device Manager
There you will find the Bluetooth adapter.
Just right click and then select Uninstall
Then I rebooted the system and installed the drivers, which I downloaded from the manufacturer's website.
If the problem persists, go to the Power Management settings.
Again, press Windows + X and select Device Manager
There you will find the Bluetooth adapter
Right click and select Properties.
Then uncheck "Allow computer to turn off this device to save power"
Now test the mouse again and see if the problem is fixed.

I have the same issue on my Dell Inspiron and Win11 update did not resolve. Though the touchpad is not effected just the Logitech anywhere 2s mouse. I think it may  be the Intel Bluetooth driver update issued mid September 21. Haven’t figured out how to rollback to verify as the rollback button is greyed out in driver window 

1. Installing Intel's Driver & Support Assistant,
2. scanning for updates in that tool, and
3. installing the Bluetooth driver

seems to have fixed the identical, recently occurring bug for me. 

Intel's Driver & Support Assistant looks promising, particularly some recent bluetooth driver fixes.

My issue was the bluetooth mouse was freezing intermittently every few seconds even when in use.

My solution was as follows:

Download and install the latest Intel® Wireless Bluetooth® for Windows® 10 and Windows 11:

https://www.intel.com/content/www/us/en/download/18649/intel-wireless-bluetooth-for-windows-10-and-windows-11.html?

This worked for me with Microsoft 3600 Bluetooth mouse

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@Valeriobsb wrote:

I would like to use my Logitech MX Master 2S Bluetooth mouse with the laptop. In fact, I have used this one a lot of months, however from the last 45 days when I use the Bluetooth mouse (as well a Microsoft 3600 bluetooth mouse), the cursor freezes every few seconds. I checked with cps test and found it stays frozen for a few seconds (usually 5 seconds) and then it starts working again. The cursor is frozen even for the trackpad. I have tried all the usual solutions - unpairing and repairing the mouse, uninstalling the Bluetooth driver and reinstalling it. I had change the power management option on the Bluetooth driver and bluetooth USB windows servides but is not works or fix it. Update all drivers recommended, and lasting update my windows 10 to 11 (hopeful that my issue was solved, and it was not. I have other laptop Asus ROG and the mouse works ok, any time.

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Had the same thing with my Logitech M705 on Windows 10. The only thing that worked was to update the Mouse driver and ensure Intel's Bluetooth driver is installed. Once done, restart the system. It's working fine since then.

Very good!! It worked for me.

Funcionou aqui com mouse Microsfot 3600 que caia com o bluetooth no windows 11

After way too much back and forth with Dell support, they sent someone out to replace the touchpad. I've had no problems since. Glad that it's fixed, but the huge pain it took to finally get Dell to replace it has hugely tarnished my opinion of Dell.

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@AdrianG001 wrote:
Then uncheck "Allow computer to turn off this device to save power"

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Came here to post this - this is what fixed it for me.

this solution worked for me on my Inspiron 14 5406, 2 in 1, Windows 11 and Dell mouse  WM524