Refactor api_access lifecycle helpers into internal modules

[tkilias]

Summary

Refactor exasol/saas/client/api_access.py into smaller internal lifecycle modules while preserving the behavior established by the preceding fixes and num_nodes work.

Problem

api_access.py has accumulated multiple lifecycle responsibilities in one large module, which makes review, maintenance, and targeted testing harder than necessary.

Proposed change

• split lifecycle logic into an internal _api_access package
• keep api_access.py as a thin facade over the internal modules
• preserve the behavior already established in the stacked predecessor PRs
• update tests as needed for the new structure and patch targets

Impact

The change is intended to be structural only. It should improve maintainability and reviewability without introducing user-visible behavior changes.

Related PR

• [codex] Refactor api access lifecycle helpers #171