Outlet/outside light dead upon plugging in air conditioner
When adding a load and multiple things quit working without tripping a breaker it is normally a back stab that has failed.
Back stabs are the push in connectors used on many receptacles , the wire is pushed in and a “edge of a metal” contact is made with the wire. Many times when heated the contact point arcs and looses connection.
Some times they start working later after cooling or vibration, but it still needs to be fixed because a heavy load will cause it to fail again.
This type of failure can be traced back to the last working device on the circuit or the first non working device. If you work from the failure working back to the breaker panel it usually only takes pulling  a couple of devices to find a loose wire or even a broken one at a connection or wire but. It can be the hot or the neutral.
If you pull out a device and did not find a problem the stab may have reconnected and the next time the ac is turned on it will open again, so I and other electricians suggest moving back stabbed connections to the screw terminals.
Just make sure to turn the breaker off when doing the work.