chore: test leanprover/lean4#6627 against #20532 (downstream cache)

[kim-em]

This uses the toolchain from leanprover/lean4#6627, @tydeu's proposed fix for the cache problems in downstream projects when using v4.16.0-rc1, and incorporates the additional CI test to simulate a downstream project from #20532.

If CI succeeds here, we will merge leanprover/lean4#6627 and include it in a v4.16.0-rc2.

[github-actions]

PR summary 333726d079

Import changes exceeding 2%

%	File
+25.00%	Mathlib.Tactic.Linter.UnusedTactic
+4.76%	Mathlib.Tactic.MinImports

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.Tactic.Linter.UnusedTactic	4	5	+1 (+25.00%)
Mathlib.Tactic.MinImports	21	22	+1 (+4.76%)
Mathlib.Data.Nat.Defs	85	86	+1 (+1.18%)
Mathlib.Data.List.Count	238	240	+2 (+0.84%)

Import changes for all files

Files	Import difference
There are 5553 files with changed transitive imports taking up over 230043 characters: this is too many to display!
You can run scripts/import_trans_difference.sh all locally to see the whole output.

---

Declarations diff

- div_le_div_left

You can run this locally as follows

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

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

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

---

No changes to technical debt.

You can run this locally as

./scripts/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).