Side note: I think you're experiencing something similar that bugs me between the mobile app and the controller I have on the wall in my hallway. The controller allows for a change in temp when I am in Dry mode, but the app does not, the same happens with Auto mode. In the app I have to do you're workaround, change the mode temporarily, change the temp and then change back to Dry mode. Given the delay I mentioned previously, I am expecting changes like that are probably applied together and sent to the unit.
In terms of your testing and at least the first log you posted, using Auto, calling the setHeatingSetPoint..... It's complicated, particularly on a Friday
But I'll take a stab at explaining it....
The way the code currently works is that if you set the heating set point, it first sets it in the heating set point state variable (on the right hand side of the device edit page). Then it checks whether you are in HEAT mode, if you are, it sends a command to MELView / the unit to adjust the set temperature, otherwise it is left unchanged. Equivalent logic is used for COOL. If you switch between modes, the set temperature would also get adjusted on MELView / the unit based on the set point for that mode.
This was the way I interpreted what Hubitat was expecting and what I had to work with on MELView. From what I could see MELView didn't have the notion of a stored heating or cooling set points, you just had a set temperature and the mode. Hubitat gave us the option to keep these separate set points, and when you switched modes, you would switch to the last set point for that mode.
Somewhat selfishly I did include Dry mode in the criteria when wanting to adjust the coolingSetPoint, but in the end I rarely take advantage of it because the dashboard tile doesn't provide that option, I tend to just do it through the wall controller or open the MELView app on my phone.
In terms of Auto... I'll need to think about it, including understanding a bit more about how the units actually operate in Auto mode and how the temperature comes into it.... But I may be able to offer another command for you to call in a rule to adjust the set temp.... But a bit more thinking involved....
On that note, I would question why you are using Auto but then adjusting the temps yourself... If you are wanting to gently decrease or increase the temperature, I would have thought you would want to let the unit operate in the mode to move the temps in that direction, with the assumption that they tend to dial back their compressor when they are around the set temperature...