Thanks everyone for the additional information. It's interesting that this is affecting such a variety of apps, including VLC, Podcast Republic, Soothing Noise Player and WhatsApp audio. That makes it seem less like an Audible-specific problem and more like something related to Android 17's handling of background media, although different apps clearly behave differently.
In my case, my ambient sound app continues to play with the screen off, but Audible still won't play in the background or with the screen off regardless of the battery settings I've tried. That difference may help identify whether the issue depends on how individual apps implement background playback.
Hopefully these reports together help narrow down what's going on.