Uncouple safe_mode from OTA

[kbx81]

What does this implement/fix?

Uncouple safe_mode from OTA

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#3841

Test Environment

• ESP32
• ESP32 IDF
• ESP8266
• RP2040
• BK72xx
• RTL87xx

Example entry for config.yaml:

# Example config.yaml
safe_mode:

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 @esphome/core, mind taking a look at this pull request as it has been labeled with an integration (ota) you are listed as a code owner for? Thanks!
_{^{(message by CodeOwnersMention)}}

[probot-esphome]

Hey there @jsuanet, @paulmonigatti, mind taking a look at this pull request as it has been labeled with an integration (safe_mode) you are listed as a code owner for? Thanks!
_{^{(message by CodeOwnersMention)}}

[codecov-commenter]

Codecov Report

Attention: Patch coverage is 0% with 2 lines in your changes are missing coverage. Please review.

Project coverage is 54.13%. Comparing base (4d8b5ed) to head (47bf42b).
Report is 655 commits behind head on dev.

Files	Patch %	Lines
esphome/cpp_helpers.py	0.00%	1 Missing and 1 partial ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##              dev    #6759      +/-   ##
==========================================
+ Coverage   53.70%   54.13%   +0.42%     
==========================================
  Files          50       50              
  Lines        9408     9619     +211     
  Branches     1654     1698      +44     
==========================================
+ Hits         5053     5207     +154     
- Misses       4056     4086      +30     
- Partials      299      326      +27     

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