feat(sdk): Refresh well-known cache in the background

[zecakeh]

Follow up to #6463, this time for the well-known cache.

The 2 last commits are for cleaning up the code a bit.

• I've documented the public API Changes in the appropriate CHANGELOG.md files.
• This PR was made with the help of AI.

[codecov]

Codecov Report

❌ Patch coverage is 86.15385% with 9 lines in your changes missing coverage. Please review.
✅ Project coverage is 89.94%. Comparing base (fd6cb66) to head (7a1ff58).
⚠️ Report is 7 commits behind head on main.
✅ All tests successful. No failed tests found.

Files with missing lines	Patch %	Lines
crates/matrix-sdk/src/client/mod.rs	85.93%	7 Missing and 2 partials ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #6480      +/-   ##
==========================================
+ Coverage   89.93%   89.94%   +0.01%     
==========================================
  Files         381      381              
  Lines      105530   105554      +24     
  Branches   105530   105554      +24     
==========================================
+ Hits        94907    94941      +34     
+ Misses       6994     6989       -5     
+ Partials     3629     3624       -5     

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[codspeed-hq]

Merging this PR will improve performance by 48.08%

⚠️ Different runtime environments detected

Some benchmarks with significant performance changes were compared across different runtime environments,
which may affect the accuracy of the results.

Open the report in CodSpeed to investigate

⚡ 1 improved benchmark
✅ 49 untouched benchmarks

Performance Changes

	Mode	Benchmark	BASE	HEAD	Efficiency
⚡	Simulation	Restore session [memory store]	166.9 ms	112.7 ms	+48.08%

---

_{Comparing zecakeh:well-known-cache-task (7a1ff58) with main (38f34e6)}

[andybalaam]

Looks good, thank you!