feat: refactor to `_useSession` semantics

[hf]

There were 2 issues with #726 which was reverted with #732:

• By accident a line was deleted in #_initialize that saved the session.
• There was a recursive-wait of #_initialize in certain cases.

This PR is the same change with some tweaks to resolve the issues. It has been tested locally. Please test before approving!

[github-actions[bot]]

:tada: This PR is included in version 2.43.0 :tada:

The release is available on:

• GitHub release
• npm package (@latest dist-tag)

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