What you are actually seeing is an Account setting, not a Power setting. Your Windows 10 is requiring a login after waking from sleep. You can fix that easily as per this (the first option): https://www.top-password.com/blog/stop-windows-10-from-asking-for-password-after-sleep/
I don't know why changing the power plan would change the login process.
I use a normal (non-administrator) User ID for my HTPC, with a password, and have it log in automatically after every reboot. Works fine, and reliably. I would advise adding a password to the account you use, and then setting it to auto login. A quick Google and you will find out how to get that auto login working.
Like you, I fail to see why changing the power plan should have any effect on the login process. However, I followed your advice and gave my HTPC user account a password. I was then surprised to find that Windows only lets you remove the requirement to enter a password after sleep when logged in as an administrator and then it applies to all user accounts, including the admin account. I was assuming it would let me make that setting at the account level, as that seems a safer approach. If I end up returning to using a Balanced power plan, I may revert to my previous user account settings where auto login worked fine.
BTW I wasn't suggesting that you permanently use the High Performance power settings, or that you never allow Sleep. Just that you compare the detailed settings between when audio works, and when it doesn't, to try to understand which setting, such as Processor Power Management Minimum Procesor State, as an example, may be causing the issue. So I would be comparing the Balanced Plan with Sleep, to the Balanced Plan without Sleep.
As the issue occurs after Sleep, something isn't being woken to the same state as immediately after a reboot, and based on your reports, never gets returned to that state. It may take a bit of digging to find out what that is.
Sadly, since my last post I experienced my audio distortion problem after twice waking up from sleep while using the High Performance setting, which has made diagnosing the cause more difficult.
BTW, I always get the following JRiver error message after rebooting my NUC. I haven't mentioned it before, as it seemed to be irrelevant to my sleep-related issues. Opening Media Center manually after a reboot seemed to eliminate any continuing problems (until the next reboot). Despite reinstalling Media Center 24 a couple of times, this problem has not gone away.
Critical error
The following module has failed to load:
C:\Program Files\J River\Media Center 24\Media Center 24.exe
It has reported the following error:
A JRiver Media Core component failed to load the product info file:
Please reinstall the latest version of the program.