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If water is coming out of the air gap, then something is blocking the
flow of water through the discharge line and into the drain, allowing
it to back up. Is all the foam gone? If there were still some left,
the foam could be backing up into the air gap and coming out, but I
tend to doubt foam could cause water to make it up through the gap.
Also, water should not be leaking underneath, sounds like the
connection to the air gap is suspect too.

Could be a pile of suds in the and with capillary action making the water
spit some. Can you pour water down the gap to clear it? What will knock
downs suds quick? If anyone has suggestions on that, I'd run a cycle of the
DW with it and that may flush it out enough.