Lighthouse will flag most of your frontend pitfalls, even post upgrade if your HTML is the same you'll get same low score as if you were on CMS11 have a closer look at the report see what improvements you can make to the front end.
Potential areas to look at
We just upgraded the site to CMS 12 using .NET 6, and while the site seems to load faster, I cannot see it in reports using tools such as Google's PageSpped or LightHouse.
This is our OLD site (with is .net framework 4.7): https://qntm02mstre747hinte.dxcloud.episerver.net/
This is the NEW site (with .NET 6 and CMS 12): https://qntm02mstr2ij5p7inte.dxcloud.episerver.net/
It seems like the site loads faster, but when I do analysis on Google's Lighthouse, I don't see any changes in the Performance scoring.
Any general guidance on how to optimize the site? And what are good tools for testing the performance of the site?