fix: Replace lossy casts with safer integer idioms

[jan-auer]

Replaces unchecked as casts and float round-trips with precise integer arithmetic and saturating conversions in four independent spots across the service and server crates.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 87.45%. Comparing base (2cc842a) to head (b5a998d).
⚠️ Report is 3 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #518      +/-   ##
==========================================
+ Coverage   87.40%   87.45%   +0.04%     
==========================================
  Files          86       86              
  Lines       13893    13897       +4     
==========================================
+ Hits        12143    12153      +10     
+ Misses       1750     1744       -6     

Components	Coverage Δ
Rust Backend	92.32% <100.00%> (+0.04%)	⬆️
Rust Client	80.07% <ø> (+0.04%)	⬆️
Python Client	88.51% <ø> (ø)

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