The interesting figure is the "Volts" number.*
Starting the A/C compressor results in immediate voltage drop, and then voltage decays further over several minutes.
Now, let's think it through. My first reaction was "ten extension cords out to a shed", but that would not explain the voltage declining over time. Also, I have faith that you would have mentioned a freakish edge condition like that.
This suggests to me several things, and we'll need to move through the list to cross them off.
Lost hot or neutral wire on the whole service
First, go to your main panel and shut off all 240V loads (double-wide or handle-tied breakers). Is the A/C circuit now stone dead? If yes, you lost a hot wire coming from the utility. 95% of the time this is the utility's fault, and they fix it for free, just call and report an outage.
Second, grab a space heater, kettle or other large 1200W+ resistive load (you want to use a resistive load for this, don't use the A/C). Turn it on, and check voltage at outlets all over the house. We're fishing for some going down with the A/C outlet but others going UP in equal measure. For instance if they are normally 118-121V, and some are measuring 109V (10V low) while others measure 129V (10V high, that's it! That is a Lost Neutral - it's the same deal as a Lost Hot, the power company needs to fix it.
Lost Neutrals are insidious, because everything seems to work - most devices will tolerate a 10-20V drop somewhat. People can have Lost Neutral problems for months and not realize it, until you have that one problem appliance that doesn't tolerate it.
Bad connections in the circuit
Most circuits are wired as a "daisy chain". Hot/neutral/ground come from the panel to receptacle 1, then from there to receptacle 2, then to a switch, then to another receptacle, etc. etc. That is a lot of connections to potentially fail, remembering that current flows in loops - so the neutral connections matter equally since they are the return loop.
A bad connection will cause voltage drop, and localized heating at the bad connection due to series arcing or resistive heating. This heat will tend to affect the connection, often making it worse. The heat takes a few minutes to develop, so it corresponds well to what you are seeing.
If you can identify all the outlets, switches, lamps etc. in the circuit, feel them all with your hand and see if any are unusually warm. Of course if the sun is beating on an outside wall and the socket is embedded in that wall with its junction box punching through the insulation, "warmer" will be natural. Anyway if you find it that easily, you win!
The most overlooked place in the whole system is the neutral bar at the service panel.
Backstab (jab in tiny hole in back of socket) connections are notorious for failing. And they are impossible to inspect. Most of us eliminate them "on sight".
The way to fix a bad connection is NOT to torque the screw gud-n-tite. You must disassemble the connection, inspect both wire and terminal for pitting or burning or soot, clean all that up, and reassemble or replace (sockets are $3, watch the tabs).
Science has shown that the torque of a screw or clamp connection really matters, even on the small stuff where it was largely ignored. It's also shown that pro electricians can't muscle-set the correct torque any better than their spouses can! (like within 1% of "too loose" vs "in spec" vs "too tight"). As a result, NEC 2014 required the use of torque screwdrivers for anything that specifies a torque, and UL started requiring things to specify torques. Electricians are not happy about this, but the science is not with the idea of "gud-n-tite is enough".
While one might argue that backstabs don't require a torque screwdriver, I'd argue side screws can be inspected.
* Obviously there are issues with the other figures, since the measured volts and amps calculates to a VA (volt-amps aka the whole sinewave the power company must deliver). And at times that is exceeded by the watts figure (the part of the sinewave the unit actually uses), giving a Power Factor well in excess of 1.00! Heat pumps can do over-unity, but not THAT way! LOL!
