The official name for the shift area piece is "shift lock override slot cover" (shrug) and I believe it is part #BHN2-64-393. Probably fits multiple Mazda vehicles. Local dealer can confirm, but the part is relatively cheap online (as low as ~$3) and you could just chance it.
Can't fully confirm the damaged interior door handle trim or sealing piece. It may be this part, but haven't cross-correlated to confirm:
There are aftermarket covers for that area in a variety of finishes, so that might be an easier solution (to just cover over it) if any are to your liking. Here's just one example that is similar to certain OEM trim (you may want to look for a US seller so it isn't as long a wait):