[CT-1847] Move `MP_CONTEXT` somewhere else.

### Describe the feature

Discovered during BLG for #6509 --

`MP_CONTEXT`, a mutex used for multi-processing, is currently stored in `flags`. This is not the right place to put that as it's definitively not a flag. Additionally, with the combining of `flags` and `args` in the api-ficiation work, we can no longer serialize flags as JSON because of `MP_CONTEXT`.

@ChenyuLInx Fixed this by removing `MP_CONTEXT` from flags before serialization, however it would be better to find it a proper place to live instead of hitching a ride on flags.

This ticket represents the work needed to remove `MP_CONTEXT` from flags and put it somewhere more appropriate.