Addendum
I have done additional research into this matter and I've found some information that is relevant to this problem.
Apple Investigations
It appears that regulators have been investigating Apple for issues like the one we are having related to their antitrust practices.
Apple Lawsuit
Currently the Justice Department, joined by 16 US States, filed a civil antitrust lawsuit against Apple for monopolization or attempted monopolization of smartphone markets in violation of Section 2 of the Sherman Act. This information can be found on the Justice Department's website at justice.gov.
Next Steps
Considering that issues like ours have been reported and ignored for over a year, the next steps for problems like this one is to reach out to the relevant authorities in order to help strengthen their case against Apple.
We will mainly do this by compiling a list of all web features which are supported by all other browser, but not supported by iOS safari listed in order of importance to a web app's success.
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Addendum
I have researched additional information which is relevant to this problem.
WakeLock Web API
The WakeLock interface of the Screen Wake Lock API can be used to request a lock that prevents device screens from dimming or locking when an application needs to keep running.
This interface, and hence the system wake lock, is exposed through the Navigator.wakeLock property.
Why this is not a solution
In this case, we want the screen to be able to sleep to conserve battery life for the user. Instead, we want the audio to play after sleep mode has ended. So this is not a solution.
The WakeLock API is supported in all browsers except Mobile Safari iOS. See bug 254545. This bug was reported to Apple over a year ago. Based on my research; the developer community appears convinced that Apple has intentionally broken this functionality in PWA environments in order to keep their App Store monopoly. These are not my views, I am simply sharing my findings.
We have the same problem. We have been giving our users a detailed explanation of why they should not use or buy Apple products. They aren't going to fix problems like this one that have been sitting on their forums for over a year.