After downloading MacOS Monterey 12.3.1 any apps that connect to the internet don't open

Try booting to Safe Mode. That boot up takes minutes and clears caches and other things that may resolve your problem.

How to use safe mode on your Mac - Apple Support

A lot of times just boot to Safe Mode followed by normal boot resolves problems.

If no problem in Safe Mode but problem returns after a normal boot that mean something is being loaded during a normal boot that is causing the problem.

If you can connect in Safe Mode but not after normal start then download and run this app so we can find more information about your installation.

https://etrecheck.com/upgrade

It shows what is launched and other information and is very useful in finding causes of problems. After you first launch the app make sure you check Enable full disk access in the box in lower left.

After running the app use the app's Share feature “Copy” that pastes to clipboard. Then paste it in the text box for a reply in this forum click on the addition text icon. This is because the normal reply text box limits how much you can type.

o personal identifiable information is contained if the app output. The app was written for a person who is contributor to these Apple Support Communities

There are no known Windows-like Viruses in the wild that self replicate and affect macOS, because of the underling UNIX  Foundation and Permission Limitation. 

The Only thing this Antivirus software is protecting is the Bank Account of the Developers and for zero return to the User aside from the problems this software creates.

The The Built in Security  is all that is required to protect the computer.

Any Third Party Applications that will interfere with the normal operation of the OS, alter, modify, remove or delete or attempt to do so is an invitation for disaster and may require a Reinstallation of the OS in-order to replace any modified, altered, removed or corrupted elements of the OS this software has inflected on this computer 

Although some or all of these Applications maybe available on the Apple Apps Store, it does not mean Apple has verified what exactly the Application can do, does do or is doing to the Computer. That responsibility is left to the User to perform their due diligence on the Application before purchasing and installing it.

Any of the below should be removed as per Developers Instructions 

This includes AntiVirus, Disk Cleaners, Disk Optimizes, UnInstaller etc.

This will included Norton Antivirus , And Read the First 600 Posting regarding the Damages this Specific Software does

Then, the user may not have read the Information provided regarding the useless Norton Antivirus

But ,that would have shown up if the user had run the Etrecheck Report

EDITED