Archery integration CI test is failing on main: error: package `half v2.5.0` cannot be built because it requires rustc 1.81 or newer, while the currently active rustc version is 1.77.2

[alamb]

Describe the bug
Example https://github.com/apache/arrow-rs/actions/runs/13864941376/job/38801863609

    Downloaded anyhow v1.0.97
    Downloaded anstyle v1.0.10
  error: package `half v2.5.0` cannot be built because it requires rustc 1.81 or newer, while the currently active rustc version is 1.77.2
  Either upgrade to rustc 1.81 or newer, or use
  cargo update half@2.5.0 --precise ver
  where `ver` is the latest version of `half` supporting rustc 1.77.2
  ERROR conda.cli.main_run:execute(125): `conda run ci/scripts/integration_arrow_build.sh /__w/arrow-rs/arrow-rs /build` failed. (See above for error)

• This is the same root cause as MSRV CI check is failing on main #7289

To Reproduce

Expected behavior

Additional context

• Also tracked by arrow monorepo ticketL: [Integration][CI] Conda Integration Test have started failing building integration testing rust arrow#45787