After some troubleshooting — including installing the app on another factory-reset phone, which worked fine — I finally figured out what was causing the issue on my device. I’m sharing this in case it helps anyone else who runs into the same problem.
In my case, the lag was actually caused by Android Auto itself. After the most recent update, it seems the location permission was automatically enabled for the Android Auto app, and this was causing MyRoute App to freeze and lag.
Interestingly, MyRoute App was the only app affected. I tested OsmAnd, TomTom, Sygic, Maps, and Waze, and none of them had this behavior.
Once I changed the Android Auto location permission to “Don’t allow,” everything started working smoothly again.
Sorry for the confusion in my earlier post, and I’m glad I can enjoy the app properly again.