Fix check config script

[balloob]

Description:

Fix check_config script being called from the async_check_config service call.

This is quite gross tbh, we should not have the core rely on anything that is inside a script. The script also has side effects like clearing the secret cache, and shares a lot of code with homeassistant.config.async_process_component_config

Related issue (if applicable): fixes #23114

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.

If the code does not interact with devices:

• Tests have been added to verify that the new code works.

[awarecan]

1000% agreed.

[codecov]

Codecov Report

Merging #23151 into dev will increase coverage by <.01%.
The diff coverage is 100%.

@@            Coverage Diff            @@
##             dev   #23151      +/-   ##
=========================================
+ Coverage   94.2%   94.21%   +<.01%     
=========================================
  Files        453      453              
  Lines      36909    36909              
=========================================
+ Hits       34769    34772       +3     
+ Misses      2140     2137       -3

Impacted Files	Coverage Δ
homeassistant/config.py	93.01% <100%> (ø)	⬆️
...ssistant/components/islamic_prayer_times/sensor.py	97.87% <0%> (+3.19%)	⬆️

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