Multi-Channel Integrated?

Not many, if any.

Multichannel integrated amplifiers are called AV recievers.

Nope …. Never even heard of one that was not already termed a “multichannel” receiver purposely segregated into their own subgroup.
With everything stuffed into a cramped unibox with limited space and cheap power supplies, we all have them and know them as fine for HT for which they do a yeoman job, but they don’t compete with high-end 2-channel with their robust power supplies for music.

OP poses an interesting question that I have wondered about myself.  In theory the only difference between a multichannel integrated and AVR is the presence of an analog tuner in the AVR.  Streamers usually handle the Internet Radio end of things so eliminating the analog tuner, and thereby having the AVR less cramped and therefore better performing, would seem to be a natural.  It’s probably due to the collapse of the home theater market in general.  Perhaps Spatial Audio will create a new demand

long long ago, the excellent Yamaha DSP-A1 multi channel integrated...still makes for a great 2 channel integrated...