Is it possible to replace the current climate control unit with an aftermarket one. I have a Pioneer radio currently in where the old head unit used to be, and having that makes the climate control look out of place. I've searched for aftermarket choices but nothing 100% comes up for it. I've seen that there are tesla type radios out there and wondering if that is an option to install into the bonneville. Thought?

Anything is possible. Is it worth the time / effort / money. Doing a tablet interface would be extremely difficult and involved.
Do you have Manual or Automatic HVAC?
Automatic is 6 wires to deal with. Manual is more complex and has around 23 wires.
Manual, the HVAC module works as the brain.
Automatic, the HVAC module is just a network device and the IPC in the dash is the brain.
It would have to be a completely custom job afaik.
First, you would need an app on the tablet. If you can program the app, you could control the inputs and outputs through an audrino or something, but realize the A/C is controlled by the PCM and communicates with the HVAC controls so that would have to be taken into account.

Another option for not interfacing directly with the inputs and outputs would be to relocate the HVAC controls and make a custom panel that replicates button presses and knob turns. Duplicating the display could be trickier, but maybe not necessary? The manual controls don't seem to have a display.

If I wanted to, and could do the app part, I would go for relocation and emulating button presses. I'm a physical button person though so i would probably go with a custom controls. Even app controlled, I would want physical backups.

I just converted my automatic HVAC from flex cable to wire and extended for relocation a little while ago.