What you’re seeing is correct to the real aircraft. The avionics for the TBM have been completely overhauled and are accurate to what you would see if you stepped onto the actual flight deck of the TBM.
You are currently on a MANSEQ leg on the departure. This means that you’re expected to manually sequence to the next leg (either by going direct-to, heading mode, or with ATC vectors). This is here because the real departure has this published instruction:
Therefore, the autopilot lateral navigation will keep you on the published 348 course until you tell it to do something else. In your case, I would just do a direct-to your next leg.