Mouse doesn't scroll/Bluetooth doesn't work on 2017 iMac Ventura 13.7.8

The message shown in System Information, “The plug-in did not respond quickly enough while gathering this information,” indicates that System Information was unable to complete gathering the Bluetooth information within the expected time.

Since Bluetooth is not currently working, first restart the Mac and check whether Bluetooth can be turned on in System Settings → Bluetooth. Apple provides instructions here: Turn Bluetooth on or off on your Mac.

If Bluetooth remains unavailable, start the Mac in Safe Mode.

While there, check whether Bluetooth can be turned on, whether System Information → Bluetooth displays information, and whether the mouse right-click functions.

Apple explains how to start a Mac in Safe Mode here: Start up your Mac in Safe Mode.

If the issue continues, run Apple Diagnostics and record any reference code exactly as shown. Apple provides the instructions for both Intel-based Macs and Macs with Apple silicon here: Use Apple Diagnostics to test your Mac.

The right-click issue may also depend on how the mouse is connected. Knowing the exact iMac model, whether it has an Intel processor or Apple silicon, and whether the mouse connects through Bluetooth, USB, or a USB receiver may help identify any further relevant troubleshooting.

Did you try to use Appel Diagnostics to test the hardware of your iMac, to see if Bluetooth is still working?

Use Apple Diagnostics to test your Mac - Apple Support

Or install macOS Ventura again via the macOS Recovery?

Use macOS Recovery on an Intel-based Mac - Apple Support

Does Bluetooth work, if you create a new user account on our Mac?

Your mouse scrolling problem and Bluetooth problem may be connected if the mouse uses Bluetooth, so I would begin by checking what macOS reports about Bluetooth.

Go to Apple menu  >> About This Mac >> More Info >> System Report >> Bluetooth. 

Note whether Bluetooth controller information and other details are displayed, or whether the section indicates that Bluetooth hardware is unavailable. 

This information may help clarify which troubleshooting steps are appropriate.

If you would like, upload a screenshot of the System Report >> Bluetooth page and we  can help interpret what it shows.

Apple's documentation confirms that a grey Bluetooth icon with a line through it indicates that Bluetooth is turned off. 

You can try turning it on in System Settings >> Bluetooth. (Apple Support)

If you are using an Apple Magic Mouse, Apple recommends checking that Bluetooth is on and, if the mouse has a compatible cable connection, connecting it to the Mac for about one minute before disconnecting it again. (Apple Support)

For additional Apple instructions on connecting and managing Bluetooth devices, see Apple's Bluetooth guide for Mac.

I would check the System Report >> Bluetooth information before making more extensive changes such as deleting system files or reinstalling macOS.