A repeat start is usually used to do a write of a command (say to set the register location), and then to do a read of that register without releasing the bus in between the read and write (Where CAPS are master, lower is from slave).
On your Logic capture, the Green dot is the start bit, the Red dot is the stop. So it is sending a repeat start, and yes that does include the address byte also.
For multi-byte writes:
(START+ADDR+W)(REG)(DATA0)(DATA1)…(DATAN)(STOP)
The only practical use of the repeat start is that it prevents another master from taking the bus in between the write and the read (the _ ). If you aren’t using a multi-master I2C bus, it doesn’t really matter. That being said, repeat starts are ‘standard’ for that scenario (as standard as anything gets with I2C anyway) and some slave ICs require a repeat start for a write-read sequence because they do an internal reset on a stop bit.
If you look at the driver for the Fuel Gauge, you can see an example. quickStart() does a register write and 2 value writes. percentage() does a register write, and then a 2 value read, utilizing a repeat start.