refactor(Geometry/Manifold/Instances/Sphere): use mvfderiv when appropriate

[grunweg]

Fixes a TODO in the file, and some pre-existing defeq abuse.
While at it, rename the affected lemmas to follow the naming convention.
There is some remaining defeq abuse in the proofs, which we comment on and localise more.

While at it, we also remove three defeq abuse options which are simply superfluous now.

---

[github-actions]

PR summary 870d68f581

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.Geometry.Manifold.Instances.Sphere	2356	2358	+2 (+0.08%)

Import changes for all files

Files	Import difference
3 files Mathlib.Geometry.Manifold.Instances.Sphere Mathlib.Geometry.Manifold.PoincareConjecture Mathlib.Topology.Compactification.OnePoint.Sphere	2

---

Declarations diff (regex)

+ MDifferentiableAt.mvfderiv
+ MDifferentiableWithinAt.mvfderivWithin
+ injective_mvfderiv_subtypeVal_sphere
+ range_mvfderiv_subtypeVal

You can run this locally as follows

## from your `mathlib4` directory:
git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci

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

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

The doc-module for scripts/pr_summary/declarations_diff.sh in the mathlib-ci repository contains some details about this script.

Declarations diff (Lean)

✅ Lean-aware diff — post-build, computed from the Lean environment (commit 870d68f).

• +4 new declarations
• −0 removed declarations

+MDifferentiableAt.mvfderiv
+MDifferentiableWithinAt.mvfderivWithin
+injective_mvfderiv_subtypeVal_sphere
+range_mvfderiv_subtypeVal

---

Decrease in strong tech debt: (relative, absolute) = (2.00, 0.00)

Current number	Change	Type (strong)
7094	-2	backward.isDefEq.respectTransparency

No changes to weak technical debt.

Current commit 870d68f581
Reference commit 5eec30bc56

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).

[grunweg]

Suggested change

	-- are not applied by simp.
	-- are not applied by simp below.

[grunweg]

This is the first location needing backcompat options (for reasons independent of this PR).

[grunweg]

This is the second one.