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

[yuanyi-350]

• refactors Cyclotomic/Basic by rewriting nonempty_algEquiv_adjoin_of_isSepClosed around AlgHom.fieldRange_eq_map and IntermediateField.adjoin_map
• replaces the manual adjoin induction with direct adjoin_le_iff inclusions for the cyclotomic roots

Extracted from #38144 , migrate from #38202

[github-actions]

PR summary 4fceb4697e

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.

You can run this locally as

./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):

• IsCyclotomicExtension.nonempty_algEquiv_adjoin_of_isSepClosed: 1.708 -> 0.664 (-61.1%)

Overall:

• The refactor speeds up the changed proof substantially.

[acmepjz]

Thank you! Looks like a great simplicifation.