Although I have used Outlook for Windows for more than two decades (Outlook 2010 and Outlook Express before that), I am not an expert. Painfully not. When I upgraded from Office 2010 to 2021 last spring, all heck broke loose and I had a lot of downtime due to mayhem the upgrade created.
Short answer from my experience is this: The upgrade process uses a wizard and goes very quickly, moving your existing .pst file from 2010 to 2022. However, as you are also on a different computer, I can't reliably help you sort that out. I suppose you may first need to install 2010 on the new computer, or at least copy your .pst file to it. If you are installing Outlook (Office) on another computer, also check your User Agreement or Microsoft to assure you're being correct.)
Definitely retain a copy or two of your original .pst file, in a separate folder, in case things go awry. In my case, things did.
Having so much email in one .pst file, and virtually no practical, substantial guidance from Microsoft on email "housekeeping" all these years, my .pst file greatly exceeded the recommended 50MB file-size limit. Long ago, I learned of an authorized tweak to the Registry that would allow a file as large as 100MB (depending on the tweak), and after that, 2010 gave me no hassle. HOWEVER, the wizard failed to preserve that Registry tweak, and the program would not install.
After several Tech rep sessions, Microsoft finally determined that we needed to restore the Registry tweak, and it installed. HOWEVER (yes, again), the installation soon crashed, requiring me to run the Repair Tool on the .pst, and ultimately requiring several days' work (and waiting days for the tool to run) and a Tech Support supervisor to rebuild my mail collection. Some of the contents are still missing, presumably sitting safely in an old .pst file. Outlook has crashed many times since, and I'll soon post separately about that.
So, short version: Install the upgrade using a copy of your .pst file, and if your email collection has created a very large .pst file, you might want to do your housekeeping first, then upgrade.
