Migrate from poetry to uv

[greschd]

Use uv for dependency management in place of poetry.

• Remove the option to build with a custom API branch. This has
  not proven useful, and is likely to be in a broken state since it's
  rarely executed. If needed, a branch can switch to using the git
  dependency explicitly in pyproject.toml.
• In CI, use explicit uv sync and uv run --no-sync to ensure only
  the expected dependency groups / extras are installed.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 93.90%. Comparing base (ce6851d) to head (ac2dd35).

Additional details and impacted files

@@           Coverage Diff           @@
##             main     #988   +/-   ##
=======================================
  Coverage   93.90%   93.90%           
=======================================
  Files         110      110           
  Lines        5902     5902           
  Branches      332      332           
=======================================
  Hits         5542     5542           
  Misses        354      354           
  Partials        6        6           

Flag	Coverage Δ
direct-launch	90.98% <ø> (ø)
minimum-deps	91.99% <ø> (ø)
python-3.11	93.07% <ø> (ø)
python-3.12	93.07% <ø> (ø)
python-3.13	93.07% <ø> (ø)
python-3.14	93.30% <ø> (ø)
server-2024R2SP5	89.53% <ø> (ø)
server-2025R1SP4	93.09% <ø> (ø)
server-2025R2SP3	93.06% <ø> (ø)
server-2026R1	93.06% <ø> (ø)
server-latest	93.66% <ø> (ø)

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