I’m fairly certain what you’re experiencing is just how lockdown mode works. It even specifically states in the menu that it’s gonna break some stuff because certain features that apps might need to function are completely disabled. The fix is “don’t use lockdown mode” because you simply cannot work around entire critical feature sets being unavailable on a system level.
To be honest, you probably shouldn’t be using lockdown mode if apps behaving weird is going to bother you. It’s an extreme measure and it says so right when you enable it, it’s not meant for casual use.