An advanced uninstallation of Logi Options+ can often resolve persistent issues. Let me know if this helps resolve the issue.
Advanced uninstall
Open terminal from /Applications/Utilities/
Copy paste the following command in the terminal sudo /Library/Application\ Support/Logitech.localized/LogiOptionsPlus/logioptionsplus_agent.app/Contents/Frameworks/logioptionsplus_updater.app/Contents/MacOS/logioptionsplus_updater --full --uninstall
Press Enter and type the admin password, press Enter again
Go to Users\Shared\ - to ensure there are no entries related to the LogiOptionsPlus app.
Go to /Library/Application Support/Logitech.localized/ - to ensure there are no entries related to the LogiOptionsPlus app.
Install Logi Options+