Voltage is generally 238-242v whenever I've checked. Got a readout on a UPS that shows incoming supply voltage.
As soon as you flip to scheduled the app shows max 16 amps immediately. I've changed the time from over night to later in the evening. Same result. I don't think it's taking into account any local load at all. It just sets the max in the app/car with no regard to it.
I've not had any other car behave like this. They've all charged the same speed regardless of whether they were on timed or charge now.
The "resting voltage" is less significant than the drop when demand rises. You will find that the voltage varies when the car is pulling the full 32amps. You can see the voltage in the Tesla app if you watch the charge in real time. An app like Tessie or Teslafi will graph the voltage over the period of the charge for easier analysis. I live in a rural area and have a long cable run to where the car charge point is located. My voltage is very variable and I do sometimes have times when the charging rate backs off.