Finder icon in the dock not responding

Does this occur for a different user, e.g., Guest ?

Consider the possibility of a third party software conflict.  EtreCheck can be used to investigate what is installed.  Give it Full Disk Access. You can post the report here. Someone might spot something.

Boot into Safe Mode according to Start up your Mac in safe mode - Apple Support and see if the problem persists. Reboot normally and check again.

NOTE: Safe Mode boot can take up to 10 minutes as it's doing the following; 

• Verifies your startup disk and attempts to repair directory issues, if needed

• Loads only required kernel extensions (prevents 3rd party kernel/extensions from loading)

• Prevents Startup Items and Login Items from opening automatically

• Disables user-installed fonts 

• Deletes font caches, kernel cache, and other system cache files

walrus549 wrote:

The finder icon in the dock is sometimes totally non-responsive to clicks. It neither opens a finder window when clicked, nor switches to a finder window if one is already open. I have tried restarting my Mac and also tried restarting in Safe Mode. In both cases the problem goes away temporarily. I have resorted to clicking on the desktop, which causes the mac to switch to Finder. Then I can open a new finder window or bring an existing finder window to the front. The icon in the dock remains unresponsive. But sometimes, after a while, the finder icon starts to work again.

Command Tab presents the heads up display for all running apps, you can navigate this HUD.

Four finger swipe down presents the exposė of all windows open for a particular app (TrackPad>Preferences>More Gestures.)

The Desktop is the active Finder by default

Command N opens your default Finder window when on the Desktop ( the default is a Finder>Preference>General)

You can relaunch the Finder on the fly, by holding the Control Option keys and click open the Finder icon>Relaunch

and see if this sorts your 'issue.'

ref:

new to Mac

https://support.apple.com/explore/new-to-mac

Get to know the Finder on your Mac

https://support.apple.com/en-us/HT201732

See and organize your files in the Finder on Mac - Apple ...

https://support.apple.com/guide/mac-help/finder-mchlp2605/mac


https://support.apple.com/guide/mac-help/dock-mh35859/mac

Use the Dock on Mac - Apple Support


https://support.apple.com/guide/mac-help/desktop-mh40612/mac

Get to know the Mac desktop - Apple Support

If you still have an issue, to sort anomalies re-install the macOS on top of your existing macOS (non-destructive)

How to reinstall macOS from macOS Recovery - https://support.apple.com/en-us/HT204904

You have a fair amount of third party software extensions/modifications. Usually in these situations incompatible third party software is the culprit. Isolating the troublemaker can be tedious. Some possibilities might include:

Trusteer

Logitech

Dropbox

AppCleaner

Backup and Sync

Garmin

OneDrive

The Dock's Finder icon is good for one Finder Window launch, and subsequent clicks on it are futile, even when those clicks are accompanied by modifier keys. You can right-click on that Dock icon and choose New Finder Window, or just revert to the simpler keyboard shortcut of command+n.

Well done.