> It is said on the manual that the jack ring would be connected to ground automatically when using unbalanced output.

True.

> Will the xlr be connected to ground and converted to unbalanced mode automatically when using trs at the same time?

No. They are driven by different op amps.

> I read the manual again. And I am a little confused: is trs a balanaced output too?

Your confusion is reasonable, because the manual is wrong...

Official ADI-2 Pro FS Spec:

1/2 TS (rear)
As output XLR, but:
Output: 6.3 mm TS jack, unbalanced

Manual Spec:

1/2 TRS (rear)
As output XLR, but:
Output: 6.3 mm TRS jack, impedance balanced

Manual Chapter 5:

"The rear of the ADI-2 Pro has 2 servo-balanced analog inputs on combo XLR/TRS sockets, 2
TS sockets as unbalanced outputs,"

Also from the Manual, Chapter 21.2:

"2 Line Out TRS 1/2
The ADI-2 Pro has two impedance balanced, short-circuit protected analog Line outputs that can
operate with levels up to +21.5 dBu (Ref Lev +19 dBu with Volume set to +2.5 dB). Using a stereo (TRS) jack the output uses two 100 Ohm resistors internally to achieve impedance balancing. Using an unbalanced mono (TS) jack ring is connected to ground automatically, the output
then operates unbalanced."

This does not make sense... MC needs to correct it...

The current manual is correct - and more up to date than the website. For a longer time already the Pro has impedance balanced TRS outputs on the rear. I will try to improve the simple overview in chapter 5.