This cable is the right type for the Raspberry Pi 7'' display.
It has the following characteristics:
- 15 core (15 leads)
- 1 mm pitch
- opposite sided contacts
- FFC / FPC cable (flat flex cable)
The original cable included in the very first display was by Wuerth Elektronik:
Wuerth Elektronik, AWM 20706 105C 60V VW-1 E328849
E328849 = UL file number
AWM 20706 does not specify the pitch. This is something to be measured on the cable itself.
Adafruit has alternative cables as well.
I'm putting this information here because it was challenging to find an authoritative source on this. It's not in the Raspberry Pi datasheet, for example.
Note: this is not for connecting to the Pi 5, you need a special adapter cable for it.