It looks like the uninstallers did not completely uninstall these softwares! I have never seen that myself, but have read in Apple Discussions about others who installed these types of utilities and then were unsuccessful in uninstalling them after advancing the MacOS. The AVAST item is truly disturbing. I am concerned one of these items that stubbornly remain is causing the TurboTax problem, although I can't be 100% sure. Although you aren't seeing anything in the Login Settings, there are many other places that launch software and processes automatically, so those items are obviously still there, somewhere.
Is this your personal Mac, or is it provided by an employer? If it is an employer provided Mac, it may be configured in a way where you cannot delete these things. If it is set up for am employer, you will need to obtain a different Mac that you set up "clean" and it will run TurboTax.
There are several things you can try now, assuming it is 100% your own personal Mac and not configured previously by someone else.
Boot into Safe Mode and try the uininstallers again. Are the residual pieces gone now?
Did you try creating a new user and try running TurboTax under that account?
Download and run Find Any File to try to search in all areas of the Mac for vestiges of these tools. You can try to then delete them but some report that the Mac's system integrity protection prevents their deletion. It is possible for a user to disable system integrity protection, delete the offending items, then reenable it, but frankly, you may be getting into some dangerous territory there since that protection is intended to protect you against deleting things in protected areas on the Mac.
If none of the above can truly rid your Mac of those intrusive software tools, then perhaps someone else here with more experience than me can suggest next steps.
I know if this was my own Mac, I would then make at least two backups, one with Time Machine and another using SuperDuper or Carbon Copy Cloner. Then I would follow Apple's instruction for resetting a Mac to factory settings: Erase your Mac and reset it to factory settings - Apple Support
Then I would set it up like a new Mac and migrate ONLY user accounts and files from one of the backups. Everything else will have to be reinstalled fresh. I feel like your Mac's system has been damaged by those security tools. The AVAST message should NOT be appearing and the VPN should have been completely uninstalled.
Before doing anything this drastic, wait to see if someone else has a better suggestion.