Possibly some help in the plumbing and parts catalog at these two sites:
Sheet 1 indicates there are two detail drawings that may help sort where you are looking at front and rear of wet bay.
Those detail drawings are on page 3 and show the parts I would guess are involved.
Suspect the flushing line has blow out at some point and now rather than the water level going high enough to drain out of the large drain fitting, the water is going out the broken/popped off flushing line?
So a look at that line might be a start?
Where that line is and how to find it is not spelled out where I can spot it, but there seems to be a small point shown on another drawing which comes from the parts catalog located here:
On the pre 2010 models we only get an older form that is just lists and exploded drawings in many cases rather than the interactive drawings we get with post 2010, but we make do!
On this one, parts are listed in groups and alphabetic order, your interest being water and sewer group, so I suggest going to the top of the index pages to get a dropdown showing page numbers, type in 252 and "enter" to quickly get down to the flushing line parts.
On that page 252 the flushing gizmo is shown and it has an air gap built in the line. What I might first guess is that when too much pressure built in the line, this line may have popped out of the fitting at some point. Since the water drains/leaks out when even a small amount of water is added, I might guess the break is low in the lineup?
Where to find it?
Does not show where I can spot it except for one small bit on page 253 next to item 10.
Would one be able to get down really low and look up under the vanity faucet to spot an openingor possible cover over an air gap?
This might be a start on locating the flush line but not too much on where exactly it needs repair.
Looking/ sorting where the water first shows may be needed to go further???