Just before lockdown 1, I went to the US and left my Tesla with one of the 3rd party valet services that operate in Heathrow. I basically did what you described.
- Drove to the Hilton supercharger at Heathrow
- Charged up to a reasonable amount (I think something like 80% or there abouts)
- Drove to the valet drop-off
- Turned on Valet mode
- Gave key card to Valet parking person
- Disconnected / logged off all apps except the official Tesla app
- Flew to the US
- Checked the car was parked, windows up, locked, etc.
- Turned Sentry Mode off
- Closed the Tesla app and didn't open it again until I got back to Heathrow