My bluetooth Logitech R500 only works in safe mode on MacBook Pro

Two things stand out from the report:

1) you should uninstall surfshark

2) you have many extensions that seem to be very old, you even have StartupItems, which is a feature that was deprecated a decade or so ago

Apple can fix Apple Accessories.

Which the Third Party Mouse Logitech R500 is Not.

Apple can’t fix the Users’ choice of Third Party Accessories use on this computer.

That clearly falls  Out-Side of the Domain of Apple

It belongs solely with the Third Party Maker of this device to make their device function on Apple Computers running Apple macOS

Not the other way around  

How to contact an app developer

If there is any comfort

Using 2 different Apple Mice and 2 different Apple Computers

They both work as expected

Since it works in Safe Mode, this indicates that probably some third party system modification is causing the problem.

Please run Etrecheck and post its full report here. Use the "additional text" button and paste the report into the text box.

Surfshark do need that sometimes however

You don't. All AV software is quite literally useless on a Mac. There no Mac viruses. None. And no AV software will stop you from installing or running a Trojan.

Shockwave, Flip4Mac, RealPlayer and Silverlight have been dead and unsupported for years. You have to go far out of your way to even find a site that still uses any of them for its content.

Aside from the already presented, good advise, for Several Contributors

We come back to the Logitech R500 Third Party Mouse and the Third Party Software, required to make this mouse function on macOS

The Third Party Software maybe updated by the Third Party Standards

Though is does not appear to updated to function on macOS macOS Sonoma 14.6.1 (23G93)

Which itself is no longer current

Sonoma 14.7.1 would be an updated version

[Running] com.Logitech.LogiFacecam.Service.plist (Logitech Inc. - installed 2024-06-09)

Executable: /Library/Application Support/LogiFacecam.bundle/Contents/MacOS/LogiFacecamService

[Loaded] com.SplitMediaLabs.LogiCapture.Assistant.plist (Logitech Inc. - installed 2024-06-09)

Command: /Library/CoreMediaIO/Plug-Ins/DAL/LogiCapture.plugin/Contents/MacOS/Assistant --timeout 300.0

Have you installed and run any "cleaning", "optimizing", "speed-up", anti-virus or VPN apps on your Mac?