My IMAC wakes up slowly, my Apple mouse will not work until I turn it off to disconnect

Download and run Etrecheck. Etrecheck is a diagnostic tool that was developed by one of the most respected users here in the ASC and recommended by Apple Support  to provide a snapshot of the system and help identify the more obvious culprits that can adversely affect a Mac's performance.

Copy the report

and use the Add Text button to include the report in your reply. How to use the Add Text Feature When Posting Large Amounts of Text, i.e. an Etrecheck Report

Before running Etrecheck assign Full Disk Access to Etrecheck so that it can get additional information from the Console and log files for the report:

Then we can examine the report and see if we can determine what's causing the problem..

Have a look at > If your Apple wireless mouse, keyboard, or trackpad isn't working as expected - Apple Support