Refactor fan platform to resemble climate/cover platforms

[oxan]

What does this implement/fix?

Refactor the fan platform to follow the design of the climate and cover platforms, which have better state handling and separation of concerns.

The current FanState class is left working, but is deprecated, so custom components should keep working.

Based on #1370, but rebased and squased to merge in the changes made to the fan model in the meantime.

Types of changes

• Bugfix (non-breaking change which fixes an issue)
• New feature (non-breaking change which adds functionality)
• Breaking change (fix or feature that would cause existing functionality to not work as expected)
• Other

Related issue or feature (if applicable): fixes

Pull request in esphome-docs with documentation (if applicable): esphome/esphome-docs#

Test Environment

• ESP32
• ESP32 IDF
• ESP8266

Example entry for config.yaml:

# Example config.yaml

Checklist:

• The code change is tested and works locally.
• Tests have been added to verify that the new code works (under tests/ folder).

If user exposed functionality or configuration variables are added/changed:

• Documentation added/updated in esphome-docs.

[probot-esphome]

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

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

Looks good to me