According to several user posts on the Pixel User Community (via Android Police), some users are claiming that when they connect a Bluetooth headset to their Pixel 2 or Pixel 2 XL handset and activate Google Assistant, it won’t detect their voice. This is despite their phones playing the alert sound to indicate that Google Assistant is listening.
So far it seems that this is a problem that has affected a variety of Bluetooth headsets, ranging from Plantronics, Anker, Beats, LG, and more, suggesting that this isn’t necessarily an issue affecting a particular brand, and could be more to do with the phones. The good news is that Google Community Manager Orrin has acknowledged that this seems to be a problem that Pixel 2 and Pixel 2 XL users are experiencing, meaning that Google is aware of the issue and at this time of posting, it appears that Google is currently trying to gather more information about it.
There is no word on how to fix it or when a fix is incoming, so until then it looks like users experiencing the problem will just have to wait.