Only log if we actually persisted LiquidityManager data

[tnull]

Previously, we logged "Persisting LiquidityManager..." on each background processor wakeup, which can be very spammy, even on TRACE level.

Here, we opt to only log if something actually needed to be repersisted and we did so (in case of failure we're logging that anyways, too).

[ldk-reviews-bot]

👋 Thanks for assigning @TheBlueMatt as a reviewer!
I'll wait for their review and will help manage the review process.
Once they submit their review, I'll check if a second reviewer would be helpful.

[codecov]

Codecov Report

❌ Patch coverage is 57.14286% with 15 lines in your changes missing coverage. Please review.
✅ Project coverage is 89.32%. Comparing base (bb5504e) to head (369ea98).
⚠️ Report is 4 commits behind head on main.

Files with missing lines	Patch %	Lines
lightning-background-processor/src/lib.rs	46.15%	4 Missing and 3 partials ⚠️
lightning-liquidity/src/lsps2/service.rs	50.00%	3 Missing ⚠️
lightning-liquidity/src/manager.rs	57.14%	0 Missing and 3 partials ⚠️
lightning-liquidity/src/lsps5/service.rs	66.66%	2 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #4246      +/-   ##
==========================================
- Coverage   89.33%   89.32%   -0.01%     
==========================================
  Files         180      180              
  Lines      138680   138745      +65     
  Branches   138680   138745      +65     
==========================================
+ Hits       123888   123939      +51     
- Misses      12172    12178       +6     
- Partials     2620     2628       +8     

Flag	Coverage Δ
fuzzing	36.00% <ø> (+0.01%)	⬆️
tests	88.69% <57.14%> (-0.01%)	⬇️

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