chore: Move group actions

[YaelDillies]

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Move the basic content of GroupTheory.GroupAction to new folders Algebra.Group.Action and Algebra.GroupWithZero.Action depending on whether it is additivisable or not.

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• [x] depends on: #12974
• [x] depends on: #13029
• [x] depends on: #13030
• [x] depends on: #13031
• [x] depends on: #13140
• [x] depends on: #13161

Once people are happy with the general idea, I will split one PR off for each new file to discuss the specifics.

EDIT: I'm hitting weird timeouts, so I guess there will be some bisecting to be done.

[Ruben-VandeVelde]

Where do you draw the line between Algebra.Group(WithZero).Action and GroupTheory.GroupAction?

[YaelDillies]

For now I'm drawing the line at "is a purely group theoretic concept". All the files I'm moving here are used in pure algebra (except Option, Sum, Sigma which instead are used in Con(NF)), but I wrote those files so yolo).

[github-actions[bot]]

PR summary 97244cb33c

Import changes exceeding 2%

%	File
+17.39%	Mathlib.Algebra.GroupWithZero.Action.Defs

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.Algebra.SMulWithZero	190	0	-190 (-100.00%)
Mathlib.Algebra.GroupWithZero.Action.Defs	161	189	+28 (+17.39%)
Mathlib.Algebra.NoZeroSMulDivisors.Defs	191	190	-1 (-0.52%)
Mathlib.Algebra.GroupWithZero.Action.Opposite	192	191	-1 (-0.52%)
Mathlib.Algebra.Module.Defs	193	192	-1 (-0.52%)
Mathlib.GroupTheory.GroupAction.Ring	193	192	-1 (-0.52%)
Mathlib.Algebra.Tropical.Basic	283	282	-1 (-0.35%)
Mathlib.Algebra.Order.GroupWithZero.Action.Synonym	321	320	-1 (-0.31%)
Mathlib.Algebra.Order.Field.Pointwise	358	357	-1 (-0.28%)
Mathlib.Algebra.GroupWithZero.Action.Basic	392	391	-1 (-0.26%)
Mathlib.Data.Finsupp.SMulWithZero	510	509	-1 (-0.20%)
Mathlib.Order.Filter.Pointwise	594	593	-1 (-0.17%)
Mathlib.Combinatorics.Additive.AP.Three.Defs	671	670	-1 (-0.15%)
Mathlib.RingTheory.UniqueFactorizationDomain.Basic	715	714	-1 (-0.14%)
Mathlib.RingTheory.Nilpotent.Basic	802	801	-1 (-0.12%)
Mathlib.LinearAlgebra.Multilinear.Basic	901	900	-1 (-0.11%)
Mathlib.Geometry.Euclidean.Sphere.SecondInter	1841	1840	-1 (-0.05%)

Import changes for all files

Files	Import difference
There are 3429 files with changed transitive imports taking up over 151899 characters: this is too many to display!
You can run scripts/import_trans_difference.sh all locally to see the whole output.

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Declarations diff

+ instance (priority := 100) MulActionWithZero.toSMulWithZero (M₀ A) {_ : MonoidWithZero M₀} - instance (priority := 100) MulActionWithZero.toSMulWithZero

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).

[mathlib4-dependent-issues-bot]

This PR/issue depends on:

• ~~leanprover-community/mathlib4#12974~~
• ~~leanprover-community/mathlib4#13029~~
• ~~leanprover-community/mathlib4#13030~~
• ~~leanprover-community/mathlib4#13031~~
• ~~leanprover-community/mathlib4#13140~~
• ~~leanprover-community/mathlib4#13161~~
• ~~leanprover-community/mathlib4#14677~~
• ~~leanprover-community/mathlib4#14705~~
• ~~leanprover-community/mathlib4#14706~~
• ~~leanprover-community/mathlib4#14851~~
• ~~leanprover-community/mathlib4#14870~~
• ~~leanprover-community/mathlib4#14871~~
• ~~leanprover-community/mathlib4#14937~~
• ~~leanprover-community/mathlib4#15430~~
• ~~leanprover-community/mathlib4#15806~~
• ~~leanprover-community/mathlib4#15983~~
• ~~leanprover-community/mathlib4#15984~~
• ~~leanprover-community/mathlib4#16440~~
• ~~leanprover-community/mathlib4#20773~~
• ~~leanprover-community/mathlib4#22121~~
• ~~leanprover-community/mathlib4#22395~~
• ~~leanprover-community/mathlib4#22512~~ By Dependent Issues (🤖). Happy coding!

[mathlib-bors[bot]]

Pull request successfully merged into master.

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