Hi, and welcome to the Apple (user-to-user) Community!
Re: "Accessibility "Background Sounds" fail to start up after wake from sleep"
Thank you for posting your information to the community, and for explaining your issue.
Am no expert in this area, yet your post deserves some response.
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Re: " I have tried disabling/re-enabling the Background Sounds and changing sounds to see if I can restart the background audio but the only solution for me is rebooting."
That was a good step to try ... If you haven't already, for more control you may want to add background sounds to Control Centre, or to the Menu bar. See Apple's online article: Play background sounds on Mac - Apple Support
Eg: says:
"Tip: You can also play background sounds from the desktop by adding the Hearing option to the menu bar or Control Centre. Choose Apple menu
> System Settings, click Control Centre
in the sidebar, then turn on Show in Menu Bar or Show in Control Centre under Hearing (you may need to scroll down). Click 
in the menu bar or in Control Centre to start and stop background
sounds, change the sound that’s playing and adjust the volume."
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Re: "Does anyone else have this same issue?"
Unless someone shares a similar experience with you here, we have no way of knowing whether or not others are sending feedback to Apple on this issue that you have. (Apple has a feedback web-page online.)
All the best :-).