Maybe a 10-558 Latch knob assembly?

Hi,

I'm trying to replace a missing latch knob assembly for a bathroom partition door but I'm unclear on what exactly is needed. I'm including photos of the door in question. The readout on the digital calipers is in inches.

Points of interest:
As you can see, and unlike some other doors I've seen, there are no guts in the door for knobs to interface with.
The door is 1.23 inches (basically an inch and a quarter) thick so I don't know if this exceeds the capacity of the 10-558, as it's indicated for "inch thick" doors. Maybe "inch thick" doors are actually 1.25 inches thick. I dunno.
If possible, it'd be nice to have the handle be ADA compliant as seen in the photo of a knob elsewhere in the building but I didn't see an indication that these are available for this type of latch mechanism. This isn't critical.
Any help you can provide would be appreciated.

Thank you,

Pedar