Qiskit / qiskit-ibm-runtime / 27194711136

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Re-organize / clean parts of utils package (#2894)

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### Summary

Revise the `utils` package, aiming to reduce the imports traversing
through it from other packages and remove unused code, as well as
focusing on reducing the amount of functionality in the really diverse
`utils.utils`:
* remove unused members
* for functions used by just one other package, move them to such
package:
   * `account.utils`
   * `api.utils`
   * moving `backend_encoder.py` to `fake_provider`
* moved the logging functionality to its own module

### Details and comments

Related to #2749

This is not meant to tackle all the possible revamps of `utils`. After
this step, `utils` roughly contains:
* utils used by the backends (backend converter, backend decoder) -
prone to be combined in a module
* utils for validation (validations and most of the items in
`utils.utils`) - prone to be combined together
* utils for a well defined purpose (deprecation, logging, default
session) - prone to stay or bubble up in some cases
* smaller functions for time conversion and other functionality used in
several places - requires more evaluation
* `json.py` - prone to be promoted to top level, requires some finesse
as it is public

Import-wise, tackling `json.py` remains the biggest source of import
complexity, and moving it out would alleviate most of the issues for
keeping a well-behaved `utils` package.

### AI/LLM disclosure

- [x] I didn't use LLM tooling, or only used it privately.

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