Add context manager for allowing unresolved templates and make the state members private

[Flamefire]

Both (templating and disabling the enforcing) should only be disabled temporarily so make the state private and expose only the context manager and a property.

2 small fixes in adjacent code:

• Use a try-except instead of an if-else (avoids an extra lookup)
• Use the resolve_template member instead of the free function to remove some C&P code

I also intended to make asdict trivial (see 2a63863) but as __getitem__ checks for deprecated parameters on each access it might impact performance too much.

Improvement after #4726