The locking is not relevant, it doesn't change whether your app remains hot/in memory or offloaded (maybe after a while, but not in itself), neither is switching between apps or opening an app from your home screen, so not sure what you mean by closing "properly"

And for hot start you shouldn't even need to tap in the document if you edited it before, the keyboard will already be opened, so the measurement is "time start, tap the app icon, tap any key, see a character appear, time end". This is a common workflow for app switching and copy&pasting from/to note app/other apps, so here even half-second delays are noticeable, and where Apple Notes shines (and only very few apps match that, but not Obsidian)

Then the cold start is where using other apps forced note app to be unloaded (or after a phone restart or "force swiping up closing" the app (think it has the same effect), here the performance difference between Notes and Obsidian is even more noticeable