refactor(NumberTheory): golf Mathlib/NumberTheory/Cyclotomic/Gal

[yuanyi-350]

• simplifies autToPow_injective in Mathlib/NumberTheory/Cyclotomic/Gal by reusing IsPrimitiveRoot.autToPow_spec instead of expanding the proof through roots of unity and pow_eq_pow_iff_modEq
• keeps the proof structured as an algHom_ext argument on the power basis, but removes the intermediate bookkeeping lemmas and coercion manipulations

Extracted from #38144

[yuanyi-350]

!bench

[leanprover-radar]

Benchmark results for 8418eab against 9268b22 are in. No significant results found. @yuanyi-350

• 🟥 build//instructions: +4.2G (+0.00%)

Small changes (2🟥)

• 🟥 build/module/Mathlib.Data.Char//instructions: +124.6M (+5.27%)
• 🟥 build/module/Mathlib.MeasureTheory.MeasurableSpace.Card//instructions: +424.2M (+3.53%)

[github-actions]

PR summary 9268b22206

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

---

Declarations diff

No declarations were harmed in the making of this PR! 🐙

You can run this locally as follows

## summary with just the declaration names:
./scripts/pr_summary/declarations_diff.sh <optional_commit>

## more verbose report:
./scripts/pr_summary/declarations_diff.sh long <optional_commit>

The doc-module for scripts/pr_summary/declarations_diff.sh contains some details about this script.

---

No changes to technical debt.

This script lives in the mathlib-ci repository. To run it locally, from your mathlib4 directory:

git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci
../mathlib-ci/scripts/reporting/technical-debt-metrics.sh pr_summary

• The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
• The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).

[yuanyi-350]

I ran a profiler comparison for the changed declarations in this PR.

Results (seconds):

• IsPrimitiveRoot.autToPow_injective: 0.117810 -> 0.032246 (-72.63%)

Overall:

• IsPrimitiveRoot.autToPow_injective elaborates substantially faster after the refactor.