Small refactoring of MQTT binary_sensor

[emontnemery]

Description:

Small refactoring of MQTT binary_sensor as proposed in #18174:

• Just store config instead of every variable since the configuration values are just copied.

Checklist:

• The code change is tested and works locally.
• Local tests pass with tox. Your PR cannot be merged unless tests pass
• There is no commented out code in this PR.

[emontnemery]

@balloob I think this is what you had in mind in #18174?

[balloob]

Yes. Looks so much cleaner I think.