As mentioned previously I have had the bluetooth problem on my M1 Mac mini. In the end I got my old wired Apple Pro keyboard and mouse. With them was packed an old Apple Bluetooth Mighty Mouse. I connected this to the mini and have had no problems with disconnection issues this passed week. Thinking Apple had solved the problem I connected the Apple Wireless Mouse and keyboard again but after 30 minutes the connection problem began again, but only with the newer products, the Mighty Mouse continued on without mishap. I am now using the wired keyboard (no disconnection issues :-) and the Mighty Mouse. In case anyone understands the system report I have included it for both mice. The main difference, to my uneducated eye, appears to be the "Bluetooth Core Spec" that is 2 on the new one and 1.2 on the old.
Address: 7C-6D-62-E7-5F-05
Major Type: Miscellaneous
Minor Type: Unknown
And the old mouse
Address: 00-1D-4F-4E-CB-B3
Major Type: Peripheral
Minor Type: Mouse
Services: Mighty Mouse
Paired: Yes
Configured: Yes
Connected: Yes
Manufacturer: Broadcom (0x2, 0x314)
Battery Level: 89%
Bluetooth Core Spec: 1.2
Firmware Version: 0x0200
Vendor ID: 0x05AC
Product ID: 0x030C
Class of Device: 0x05 0x20 0x2580
AFH: On
AFH Map: FEFFBFFFFFFFFF77CE3F
RSSI: -70
Role: Master
Connection Mode: Sniff Mode
Interval: 11.25 ms
Host Connectable: Yes
EDR Supported: No
eSCO Supported: No
SSP Supported: No
Services: Apple Wireless Mouse
Paired: Yes
Configured: Yes
Connected: Yes
Manufacturer: Apple (0x3, 0x31C)
Battery Level: 100%
Bluetooth Core Spec: 2.0
Firmware Version: 0x0084
Vendor ID: 0x05AC
Product ID: 0x030D
Class of Device: 0x00 0x00 0x0000
AFH: On
AFH Map: FEFFBFFFFFFFFF77CE3F
RSSI: -56
Role: Master
Connection Mode: Sniff Mode
Interval: 11.25 ms
Host Connectable: Yes
EDR Supported: No
eSCO Supported: No
SSP Supported: No