"USB Accessories Disabled" notification from Thunderbolt 3 network connection?
Is the Air trying to charge itself from the MBP over Thunderbolt?

That is quite possible.

How can I get it to stop, or at least to stop the notification from
appearing?

As I recall a MBP can source up to 15 watts to no more than two USB-C ports, and no more than 7.5 watts to the other two ports.  Apple laptops can sink power from only one USB-C port at a time.  If there is more than one power source connected then the laptop will choose to sink power from the source that is advertising the ability to source the most power.  If there's two sources advertising the same power output capability then it will choose one at random.  An Apple laptop will not typically switch from one source to another if both are of equal capability but if something should interrupt the connection to the first choice then it might flip.  An interruption might be from the laptop being put to sleep and reawakened, a reboot, a loose cable, a utility power glitch, or something else attached to the power source taking enough power that it changes it's advertised power ability.
Considering the MBA side of this connection first there's looking at where it should be getting power.  The first obvious thing to check is for loose cables.  I'll see docks and displays with more than one usable USB-C port to the host, where one supplies more power than the others.  Is the MBA connected to the high power port?  A low power port will supply 15 watts just like the MBP would, it wouldn't take much to trigger the MBA to flip to take power from the MBP.  Even if the MBA is connected to a dock, power brick, or display that advertises 60 watts of power available a glitch in the system could cause a flip.
On the MBP side there could be USB power issues other than the power hungry drives and video camera.  Consider what else is plugged in.  Consider that if the MBA is drawing power that it's going to want to take all 15 watts the MBP could give.  Given that you are not seeing the MBP try to sink power from the MBA it's likely that the MBP has a solid power source.  Or, it has a 96 watt power brick and a display capable of sourcing 60 watts connected that it's not likely to try getting 15 watts from the MBA.
I can certainly agree that it's not certain that the connection to the MBA is the problem but you did make a case on that being a place to look.  What would be helpful is to find a way to maintain this Thunderbolt connection but in a way that no power can travel down that wire.  That's not going to be easy, or at least not cheap.
One way to break that power connection and keep the Thunderbolt connection is with two Thunderbolt 2 adapters and a Thunderbolt 2 cable.  That's putting what is likely a $15 cable into a drawer and replacing it with a cable and adapters that would cost about $150.  Oh, and it would cut the bandwidth of the connection in half.  Perhaps with a steady hand and a sharp knife someone could do surgery on a $15 cable to remove the wires that transfer power and not disturb the wires needed for a Thunderbolt connection.  An optical Thunderbolt 3 cable would give full bandwidth and have no power transfer.  An optical Thunderbolt 3 cable would cost a lot of money too.  Is there a means to get Thunderbolt without power delivery that I'm missing?  If it's possible to borrow a couple Thunderbolt 2 adapters and a cable then you could at least test the theory.  Borrowing an optical cable would also work but likely be far more difficult.
I suspect that using anything other than a Thunderbolt cable to connect the two laptops is undesirable.  A Thunderbolt 3 cable is a very cheap and very fast way to connect two Apple computers.  There's just nothing else like it.  Opening up the set of acceptable solutions to those that include removing the Thunderbolt connection will likely bring a solution faster.  But then that makes it so trivial that there's not much to discuss.