`Coordinates` operations

What is your issue?

At the moment, the Coordinates objects are not as useful as I'd like them to be, so in this issue I'd like to collect all the methods it should support. Some of these already exist, but listing them again helps with defining a coherent API:

• coordinate variables
  • assignment of new coordinates (from Variable / DataArray / Coordinates / any array): Coordinates.assign()
  • deletion of coordinates (similar to Dataset.drop_vars): only via del coords["x"] but a Coordinates.drop_vars() might be welcome I guess
  • renaming coordinates: no specific method yet, Coordinates.rename_vars()?
  • renaming dimensions on coordinates: no specific method yet, Coordinates.rename_dims()?
• indexes
  • assignment of index instances: could use Coordinates.assign(Coordinates.from_xindex(idx_obj)) but one index at a time
  • dropping indexes: Coordinates.drop_indexes() (#8118)
  • creation of an index based on variables, a given class, and additional options: Coordinates.set_xindex() (#8118)
• combination
  • merging (also using |)

cc @benbovy, @scottyhq

Start by reviewing the existing Coordinates API and the unchecked operations listed in the issue, especially Coordinates.assign() and index assignment. Read the related drop_indexes() and set_xindex() work in issue #8118, then compare it with the existing deletion, renaming, and merging behavior. Done would require an agreed, coherent Coordinates API for the remaining operations.