Erin Stellato has an experiment with Query Store plan forcing:
A question came up recently about plan guides and compatibility mode, and it got me thinking about forced plans in Query Store and compatibility mode. Imagine you upgraded to SQL Server 2016 and kept the compatibility mode for your database at 110 to use the legacy Cardinality Estimator. At some point, you have a plan that you force for a specific query, and that works great. As time goes on, you do testing with the new CE and eventually are ready to make the switch to compatibility mode 130. When you do that, does the forced plan continue to use compatibility mode 110? I had a guess at the answer but thought it was worth testing.
There are some interesting results here.