Google started selling audiobooks several days ago. If you haven't tried them yet, that is okay because you are better off avoiding Google in favor of a retailer that cares about selling audiobooks and actually invested time in providing a good experience.
For starters, the Play Store website itself is pretty basic, with zero sorting options (like price or publication date) for audiobooks. You're stuck with Google's idea of the best way to discover a new title, or you are welcome to leave.
As for listening to audiobooks, you can technically listen to an audiobook in the Play Books app - if you can find the audiobook first. I have updated the Play Books app, but on my older Android phone there is no mention of audiobooks anywhere. (I can play audiobooks on the phone, yes, but they are not shown anywhere in the library.)
According to a friend, there is supposed to be a tab for audiobooks:
When I first opened it, there was no "My Audiobooks" or anything, that only showed up after I bought a book. It works, but it looks like the minimum possible work went into the whole thing. On the web, again, there isn't a "My Audiobooks" section, I had to go into the page for the book I bought, where "Buy" became "Play".
The only way I can play an audiobook is on the notifications pulldown screen.
Edit: And after I rebooted my phone in the hopes that the new features would appear, that option vanished. So now I have an audiobook on my phone and no way to play it.
Edit: And it turns out I can't store audiobooks on my SD card, which means I will only be able to carry one or two audiobooks at best on my phone's limited internal storage.
Before anyone jumps into the comments to blame my problems on my old phone running an old version of Android, I'd remind you that there are still a lot of older Android smartphones out there ruining old OS versions, and judging by my experience those older phones don't really support the new audiobooks.
If Google isn't supporting older phones then the user experience is going to be pretty awful for most people. They would be better off using Audible or another app made by a company that cares about selling audiobooks.
Google clearly does not.