Make background-processor NO_* constants actually Send + Sync

[TheBlueMatt]

In 0d59d73 we added constants to better enable users to call background processor methods without optional parameters. Sadly, they didn't work for the async BP as they weren't actually Send + Sync, which we fix here.

[ldk-reviews-bot]

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[codecov]

Codecov Report

❌ Patch coverage is 93.33333% with 2 lines in your changes missing coverage. Please review.
✅ Project coverage is 88.60%. Comparing base (19a9dbd) to head (e040fcd).
⚠️ Report is 2 commits behind head on main.

Files with missing lines	Patch %	Lines
lightning-background-processor/src/lib.rs	93.33%	1 Missing and 1 partial ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #4132      +/-   ##
==========================================
- Coverage   88.63%   88.60%   -0.03%     
==========================================
  Files         180      180              
  Lines      134878   134904      +26     
  Branches   134878   134904      +26     
==========================================
- Hits       119543   119535       -8     
- Misses      12567    12601      +34     
  Partials     2768     2768              

Flag	Coverage Δ
fuzzing	21.76% <ø> (ø)
tests	88.44% <93.33%> (-0.03%)	⬇️

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[tnull]

Should we also add some test coverage for this case then?

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[TheBlueMatt]

Fixed the no-std build and added test coverage.