Hi clasmon,
Welcome to Apple Support Communities. It sounds like you've tried some great steps and that your settings are correct. It might be helpful to test another auto lock time increment to see if the same happens there. That might isolate this further.
We'd also recommend using the guidance in About iOS or iPadOS performance on your iPhone, iPad, or iPod touch since this might be related to an underlying performance issue due to storage, battery, etc. All guidance there will be helpful but storage and battery might be something to examine closely. We've included those tips below.
"Make sure you have enough storage
If your device is low on storage, iOS or iPadOS automatically frees up space while installing an app, updating iOS or iPadOS, downloading music, recording videos, and more. iOS or iPadOS only removes items that can be downloaded again or that aren't needed anymore.
You can check your device's storage in Settings > General > [Device] Storage. For best performance, try to maintain at least 1GB of free space. If your available storage is consistently less than 1GB, your device might slow down as iOS repeatedly makes room for more content."
"Leave Low Power Mode off when you don't need it
Low Power Mode is an iPhone and iPad feature that extends battery life by reducing the amount of power that your device uses. In Low Power Mode, some features are turned off and some tasks might take longer to complete. If your battery icon is yellow, that means Low Power Mode is on.
Consider leaving Low Power Mode off if you need your iPhone or iPad to function without low-power restrictions. You can turn Low Power Mode on or off in Settings > Battery.
Get more information about Low Power Mode."
"Look at your battery health
All rechargeable batteries are consumable components that become less effective as they chemically age. Over time, the rechargeable batteries in all iPhone models will diminish in their capacity and peak performance and will eventually need to be replaced. iOS can show show battery health and recommend if an iPhone battery needs to be replaced. Go to Settings > Battery and tap Battery Health. Battery Health is available only on iPhone.
Check your iPhone battery."
Best of luck.