"Unable to find specified template or user doesnt have permissions to read it"
This should have nothing todo with the version upgrades. Do you see the template in the studio when you log in with the same user that is doing the API request?
I've added those versions to the original post above.
As far as I know, jsreport v2 should run fine in node 12. There are just known problems in jsreport v2 with import and office recipes with node 16.
The ubuntu later than xenial breaks https resources like images when you use phantom-pdf recipe. However, you most likely already use the chrome-pdf recipes introduced in v2 so you should be fine.
In every case, this wouldn't cause the mentioned error Unable to find specified template which means the template rendering even didn't start because the template wasn't found.