[SERIALIZE] Make serialize uniform and usable

[blythed]

There are several ways in which serialization is not the same in several places:

• Different between SQL & MongoDB (Schema vs inline).
• Different between how users would "create" a serialized version from scratch _leaves.
• The way queries are serialized isn't the same as other classes.

Serialization is also not "usable":

• The nested dict isn't sustainable for users.
• Separation of cls and module unnecessary.

This should be made symmetric and usable.

• [ ] #2028
• [ ] #2029
• [ ] #2030
• [ ] #2031
• [ ] #2032
• [x] #2042
• [ ] #2043
• [x] #2044