Regressed queries after statistics update
These are the steps I would take:

First of all download Microsoft Migration Assistant and try to spot incompatibilities between compatibility level 2008 and 2012.
Then download Microsoft Assessment and Planning Toolkit and scan for all sort of incompatibilities following a guide.
Spot the incompatible queries using the Query Tuning Assistant .
If everything is alright now move to 2012 compatibility level first and check if all the applications are still working. If the database is old I suppose the applications bight be old too. The applications may contain deprecated command not compatible with later version of SQL Server
If the previous step worked now move to compatibility level 2016 and activate Query Store. Use that to monitor your database for a good week or two and check if everything is alright. At this point 99% of your queries should run faster and 1% should be completely blocked. Query Store is your friend and you will use it to debug blocking and waits.
Now that everything is fixed moving to compatibility level 2019 should be a glass of water as there are not many changes between 2016 and 2019