I have one USB dongle with VIA VT1620A.
Probably unobtainium as an individual IC
Yeah indeed.
I'm sure there are many others; search around for ICs marketed for USB soundcards or headsets and the like.
Single-chip USB + DAC + ADC aren't that many actually. The very cheap USB audio cards available are almost all using C-media parts. There may be even cheaper obscure chinese chips, but I don't know. And availability is probably even worse in Europe.
Most of the less cheap cards use a separate USB IC and Codec (ADC+DAC) IC.
We'd need to know what's the rationale for a single-IC solution here. Is it for cost reasons, or for PCB area reasons? Or availability, as finding one available IC might be safer at the moment than having to deal with two?
Because as far as cost and availability goes, it would probably be easier and even cheaper at this point to design a 2-chip solution. The USB-I2S part could even be implemented on a cheap MCU to further lower cost and increase your chances of availability; cheap Codec ICs are many, so that's not much of a problem.