[backport] Retroplayer: Savestate manager fixes

[KOPRajs]

Description

This is a backport of #22490 to Nexus.

I was originally hoping to have this merged by the time the Nexus is released, but better late than never.

Motivation and context

How has this been tested?

What is the effect on users?

Screenshots (if appropriate):

Types of change

• Bug fix (non-breaking change which fixes an issue)
• Clean up (non-breaking change which removes non-working, unmaintained functionality)
• Improvement (non-breaking change which improves existing functionality)
• New feature (non-breaking change which adds functionality)
• Breaking change (fix or feature that will cause existing functionality to change)
• Cosmetic change (non-breaking change that doesn't touch code)
• None of the above (please explain below)

Checklist:

• My code follows the Code Guidelines of this project
• My change requires a change to the documentation, either Doxygen or wiki
• I have updated the documentation accordingly
• I have read the Contributing document
• I have added tests to cover my change
• All new and existing tests passed

[garbear]

I've tested this PR on my Nexus branch with the changes in #22585 applied. Everything works as expected so far.