Isn’t this the common issue that is expected behavior since the WT update to the Garmins?
In other words, you are trying to use the Garmin GPS in the old way instead of the new (realistic) way.
Can you double check? Symptoms sound like you just forgot to flip the AP master switch on the top panel.
I’ve been flying the TBM regularly and I’ve never had a problem with the FMS NAV AP.