Simplify Overkiz coordinator (step 2) and address feedback

[iMicknl]

Proposed change

As mentioned in review feedback #62640 (comment), the coordinator is too complex and hard to read. In previous PR we removed some parts, in this PR we will implement the Registry() helper as suggested.

Not sure if this is the right way with passing self, however we need access to our data coordinator class variables

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[probot-home-assistant]

Hey there @vlebourl, @tetienne, mind taking a look at this pull request as it has been labeled with an integration (overkiz) you are listed as a code owner for? Thanks!
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[tetienne]

Really nice cleanup 💪

[iMicknl]

We moved the logic 1:1, this is the only function that has been changed. Last PR's we really made it complicated to pass mypy, but now it was possible to simplify this and keep 100% mypy strict.

[MartinHjelmare]

Nice!