[safe_mode] Allow user-defined interval for successful boot

[NMartin354]

What does this implement/fix?

Adjusts the reboot timeout to a single function instead of serving two functions

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#3930

Test Environment

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

Example entry for config.yaml:

# Example config.yaml
ota:
  password: !secret ota_password
  reboot_timeout: 5min
  attempt_timeout: 5min

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 @jsuanet, @kbx81, @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)}}

[kbx81]

In the doc update, you refer to attempt_timeout but have not exposed that configuration variable to the user via config. Please update this PR to do so.

Also, all CI/tests must be passing before we will review the PR. Thanks for working on this!

[codecov-commenter]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 53.91%. Comparing base (4d8b5ed) to head (81888b2).
Report is 737 commits behind head on dev.

Additional details and impacted files

@@            Coverage Diff             @@
##              dev    #6882      +/-   ##
==========================================
+ Coverage   53.70%   53.91%   +0.20%     
==========================================
  Files          50       50              
  Lines        9408     9625     +217     
  Branches     1654     1698      +44     
==========================================
+ Hits         5053     5189     +136     
- Misses       4056     4112      +56     
- Partials      299      324      +25     

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[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)}}

[NMartin354]

I appreciate you taking care of it for me.

Just for growth, I committed the init.py twice and it still fell through, was that my fault?
(First pull)

[jesserockz]

@NMartin354 Aha, I just took a look at your fork, and you pushed it to a new branch which made it not part of this pull request.

The real fault lies in creating the original work and pull request on your fork dev branch. You should always make a new branch for any piece of work and make the pull request on that branch.