I don't believe there is any link between B0441 (Left Actuator out of range) HVAC, and the fuel gage issue. Probably coincidence.
The HVAC electric actuators go through a power up test and calibration check when first connected to battery power. This test initializes the HVAC control assembly by driving the damper doors fully open and closed while calibrating their range of motion.
( they both use feedback pots to monitor the door position).
If it were me, I would first clear the codes and then disconnect the battery for a few moments, and then reconnect it. This would cause the test proceedure described above to run. After completion check for codes and then see if air runs cold.
Also check for PCM P1431 error code. That's the one that usually sets for a fuel sending unit problem, which by the way is very common. Search on "fuel gauge" for lots of posts on any C5 forum.
Let us know.