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Almost all smart speaker use omnidirectional MEMS microphones. They are small, good and inexpensive. Something like this perhaps: https://www.digikey.com/product-detail/en/knowles/SPW0690LM4H-1/423-1423-1-ND/8573349
You won't find these with a USB interface, they are either analog, PDM and in rare cases I2S.
Keep in mind that smart speakers have multiple ...
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It is sometimes possible, but not advisable, to transmit from a wireless audio transmitter designed by one manufacturer, to a wireless audio receiver made by a different manufacturer.
Cross-manufacturer compatibility is much, much more likely to succeed when both transmitter and receiver are analog wireless ("FM"), and much less likely to succeed when both ...
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