The Nemo version in the Focal Repos is 4.4.2.
I used Nemo when I was on Zorin OS 16 (Focal) throughout with no freezing or lagging. So, there may be a different issue causing the lag or freezes.
You can upgrade Nemo using the means of the LinuxMint Daily Builds repository, but must remember to remove the repository once Nemo is installed. We have seen above what can happen if the repository is retained, then the system upgrades run - the MintSources package will be installed due to the repository being its source. The MintSources package is not able to know what system you are on and will assume you are on the latest Mint. It will treat your O.S. like it is the latest Mint. And this will conflict with Zorin OS.
I also need to be very clear here about what Nemo is.
Nemo is not just a standalone file viewer. Nemo is an integral part of Desktop Environment management and it, like Nautilus or Thunar, manages many aspects of the Desktop itself. This being the case, a user would be ill-advised to treat it as a package that can be upgraded to a different dependency version than the Base Desktop. You are asking for version Nemo 6, without showing any indications whatsoever for what features it has that you need... And this suggests your motive is in having the latest and greatest just for the sake of having it.
The file manager is part of the Desktop and if you want or need the latest version, you must use it on the desktop it is built to be used with: Mint Cinnamon. Nemo is versatile and stable enough that Nemo 5 works very well on Zorin OS 16; but a user should not punch into the boundaries aimlessly.
Now, when I used Nemo 4.4.2., I never had any performance issues. However, the advent of Nemo 5 brought an advanced file search functionality that I wanted.
In order to properly use and maintain my machinery, the onus is on the user to learn what is needed to do so. This applies to you just as much.
I can only offer limited support at this time.
If this was me, with my machine, I would re-install the O.S. after making back ups and preparing myself mentally for cleaning house and enjoying a fresh install. Mistakes and following a learning curve are a part of life; on any O.S., any computer and in any activity or any relationship. A restart can work wonders.
With a re-install and without repeating the mistakes made that taught some lessons, you may attain greater stability with your computer.