Catalina startup is very slow and finding sites is also very slow

1 - Suggest restarting in Safe Mode. This will perform a Disk Repair, clear cache files and only load Apple Software, extensions and fonts. The boot up will be slow and can take some time - Normal.

2 - Does the issue present in this mode ?

3 - If not - there could be something in the main User Account playing up. To further isolate this - Set up users, guests, and groups on Mac. Then log out of the Main User account and log into the dummy account and test again if the issue persists.

4 - If the issue is present in the dummy account - then this appears to be a System Wide issue.

5 - Suggest downloading the Application Etrecheck directly from a well Respected ASC Contributor. And Safe to use.

The application is free or paid from added features. 

Run the application with Full Disc Access ( Security & Privacy - Full Disc Access ).

It will take a Snap Shot -  both the hardware and software.

 The Report will Not Reveal Any Personal Information. 

Post back the Full Report - copy and paste - using the Additional Text Icon ( 3rd Icon to last )

We can have a look at the report for possible issues and may have possible suggestions to resolve the issues.

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.

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

This will include CleanMyMac 

This will include BitDefender 

This will included Norton Antivirus

Sophos Av Software

Intego AntiVirus

McAfee

MacKeeper

Avast AntiViru 

Ad Guard

The The Built in Security  is all that is required.

This computer may qualify for macOS Catalina is compatible with these computers

For sure it does not Qualify of Bug Sur and Monterey as per below

Computer Qualify for the Monterey upgrade

macOS Big Sur 11 hardware requirements

Is this a New Issue ? If Yes, what exactly changed on this computer ?

Is this an Old Issue ? If Yes, what actions has the user taken to fix this issue ?

Reliable , accurate, details and context will really help to pinpoint a possible solution.

@R. Philips :

Please forgive my out of initial topic question. But you are a serious user here.

Your screen capture shows that "Software Update" has "Full Disk Access" turned off.

Wouldn't this setting cause you future problems with next system update or upgrade?

I would name this tuning "security turned too high".

After following the @R. Philips answer with Safe Mode,

like you, I would suspect a painful disk reconstruction at startup.

One easy trick to confirm this is to boot with a console telling you what is going on

so as to witness the culprit in action. This is also a method to become more computer proficient.

Boot your iMac, and immediately jump on [⌘]+[v]. Here [v] stands for verbose.

You will discover the real truth about what's hapening during an OS boot.

Don't be afraid by the old console look.

You will perhaps recognize warning or error messages about your internal disk,

perhaps during many minutes. Sorry for this possibility of bad news.

Sometimes the truth hurts.

You can use the suggested Verbose Mode as suggested by previous posting.

Suggest you read this article to understand the extent of what it can do and not do.

How to Boot in Single-user Mode or Verbose Mode in macOS and as the article outlines - it is best used by Advance Users and even then, the information gained in Verbose or Single User Modes is bet left to Apple Software Engineers to really understand.