What about open source? I'm not buying apps anymore that are closed source. It can even be a zip file that comes with the app or a https://sr.ht repository, literally anything
I would also be happy to help you configure fdroid!
Vivid Navigation Gestures worked for me (same developer as Immersive Mode Manager)
https://play.google.com/store/apps/details?id=com.ivianuu.oneplusgestures
Having explored this further it appears to be caused by the app Fluid NG (beta version). Disabling the app allows Immersive Manager to persist after screen off/on.
https://play.google.com/store/apps/details?id=com.fb.fluid
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Interestingly, your own gestures app, which performs a similar function to Fluid NG appears to work fine.