fix: Reverse Proxy support

[Degot]

Description

These changes allow to use sunshine webui after reverse proxy with subpath.

Screenshot

Issues Fixed or Closed

• Resolves WebUI can't be used as subpath behind Nginx reverse proxy #3008

Type of Change

• Bug fix (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)
• Dependency update (updates to dependencies)
• Documentation update (changes to documentation)
• Repository update (changes to repository files, e.g. .github/...)

Checklist

• My code follows the style guidelines of this project
• I have performed a self-review of my own code
• I have commented my code, particularly in hard-to-understand areas
• I have added or updated the in code docstring/documentation-blocks for new or existing methods/components

[ReenigneArcher]

Perhaps, along with this PR, it would be good to update the docs with a simple example of how to use Sunshine in a reverse proxy? I think it would make sense to go here: https://github.com/LizardByte/Sunshine/blob/master/docs/guides.md , under a new ## General section.

[ReenigneArcher]

Perhaps, along with this PR, it would be good to update the docs with a simple example of how to use Sunshine in a reverse proxy? I think it would make sense to go here: https://github.com/LizardByte/Sunshine/blob/master/docs/guides.md , under a new ## General section.

@Degot any thoughts?

[sonarqubecloud]

Quality Gate passed

Issues
0 New issues
0 Accepted issues

Measures
0 Security Hotspots
0.0% Coverage on New Code
0.0% Duplication on New Code

See analysis details on SonarCloud

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 11.13%. Comparing base (fc78f5a) to head (116354f).
Report is 82 commits behind head on master.

Additional details and impacted files

@@           Coverage Diff            @@
##           master    #3173    +/-   ##
========================================
  Coverage   11.13%   11.13%            
========================================
  Files          99       99            
  Lines       17211    17211            
  Branches     8023     8023            
========================================
  Hits         1916     1916            
- Misses      12594    12737   +143     
+ Partials     2701     2558   -143     

Flag	Coverage Δ
Linux	8.42% <ø> (ø)
Windows	5.19% <ø> (ø)
macOS-13	13.61% <ø> (ø)
macOS-14	12.60% <ø> (+0.01%)	⬆️

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see 22 files with indirect coverage changes