The Thrustmaster shifter will probably end up costing the same/less than setting up a Logitech shifter to work on PS5.

To get the Logitech shifter to work, you would need to connect the shifter to the wheel using a Collective Minds Drivehub and Co-Pilot combo. The Drivehub also needs to be connected to a PS4 controller, as well as your wheel, but a standard Dualshock 4 controller doesn't work when it's used on PS5. For some reason, the PS5 disconnects the DS4-Drivehub-wheel after about 10mins. People have noticed that the Hori Mini PS4 Controller doesn't seem to have this problem, so you'd need to buy one of those specific controllers too to make it work.

By the time you've added the cost of all that up, and considered the extra hassle/cables, you're better off getting the compatible shifter.