Paired Bluetooth speakers don't always automatically connect to my Mac mini

Excuse this post but I have just tried AI on a whim and got these suggestions which sound plausible though I haven't tried them.

"The issue is likely a macOS energy saving setting that is disconnecting the Soundcore Mini after prolonged inactivity. To address this, you can try:

1. Adjusting macOS Energy Saving Settings:

• Find the relevant setting:
• On your Mac, go to System Preferences (or Settings in newer macOS versions) -> Power Adapter -> Automatic Power Off.
• Modify "Allow sleep" settings:
• Make sure the "Allow sleep" option for the display and the computer itself are set to a time that is longer than your typical use. This will prevent the Mac from going into sleep mode too quickly.

2. Unchecking "Disconnect Bluetooth After Sleep":

• Open Bluetooth settings: Go to System Preferences (or Settings) -> Bluetooth.
• Check "Disconnect Bluetooth After Sleep" checkbox: Uncheck this option if it's enabled.

3. Resetting the Bluetooth Module (Advanced):

• Reset the Bluetooth module: If the above steps don't work, you can try resetting the Bluetooth module on your Mac. To do this, hold down the Shift and Option keys while clicking the Bluetooth icon in the menu bar, then choose "Reset the Bluetooth module." 

4. Other Troubleshooting Steps:

• Ensure the speaker is charged: Make sure your Soundcore Mini is fully charged.
• Check for software updates: Make sure your Mac and the Soundcore Mini have the latest software updates.
• Consider using a wired connection (if available): If possible, use a wired connection instead of Bluetooth to see if the issue persists.

5. Specific to macOS:

• Delete and Re-pair:
• You can try deleting the Soundcore Mini from your Mac's Bluetooth list and then re-pairing it.
• Check for Third-Party Software Conflicts:
• Some third-party software can interfere with Bluetooth connections. Try disabling or uninstalling any software that might be causing issues. 

By addressing these potential causes, you should be able to resolve the Bluetooth connection issues with your Soundcore Mini and Mac after prolonged inactivity."

I have been having a similar problem for several years with a small Anker SoundCore speaker.

It's OK after brief periods of sleep but overnight it will definitely lose its connection.

Never found a solution.

Having studied the AI comments I feel they may be generalised garbage as some of the suggested settings do not appear on my Mac!

The only strategy I have found that usually worked was to switch off the speaker and back on again whereupon with luck it would reconnect automatically.

Sounds like maybe the bluetooth speaker system is still be paired with the PC, an iPhone or something else and not discoverable when you first startup the Mac mini.