I don't know how to adjust the Windows dialog to display that (there might be a Registry setting buried somewhere), but it's always been confusing when we're switching to new versions. I want to set file associations to always go to the new program... but which is the new one? Trial and error.
In your case where you're regularly getting the prompt, the only option I know is to pin program shortcuts to your Taskbar, add them to your Start Menu, or create keyboard shortcuts to quickly open the program you want first and then you'd just drag your .dwg file into the appropriate program.
Work: AutoCAD 2022.1.3, Windows 10 Pro v22H2 64-bit, Intel Core i7-8700K, 32GB RAM, Samsung 960 Pro SSD, AMD Radeon Pro WX 5100, 3 Dell Monitors (3840x2160)
Home: AutoCAD 2022.1.3, Windows 10 Pro v22H2 64-bit, Intel Core i7-11700, 64GB RAM, Samsung 980 Pro SSD, NVIDIA Quadro P2200, Dell Monitor (3840x2160)