Bump dependencies, refactor slightly to LieGroups.jl

[kellertuer]

This is an approach to refactor the Lie solvers to LieGroups.jl

I noticed that the ManifoldLieSolver had a manifold stored, but the action has that stored as well, I think even had before, so I removed the manifold field.

But one think I a struggling with is that there are now 3 places where allocation fails (one(::Any) not defined). This happens when using diff_group_apply - and I do not see why that now fails (maybe allocation with identity does not work?) nor why that diff is used in the first place, since the formulae are not documented.
To the rescue @mateuszbaran ;)

📋

• bump dependencies, include LieGroups.jl
• Switch to using Runic.jl
• setup DocumenterInterlinks
• setup DocumenterCitations if that is not yet present.
• check that in the docs the ManifoldEuler is more prominent and gets its own problem
• understand and document the Operators a bit better.
• add NEWS.md entry

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 92.62%. Comparing base (d61851a) to head (15af04e).
⚠️ Report is 1 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main      #41      +/-   ##
==========================================
+ Coverage   92.59%   92.62%   +0.03%     
==========================================
  Files           8        9       +1     
  Lines         486      488       +2     
==========================================
+ Hits          450      452       +2     
  Misses         36       36              

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[mateuszbaran]

I've fixed the tests and made some updates to the documentation. The documentation is indeed a bit minimal and it's currently necessary to reference the papers to understand what is happening here but that could also be addressed in a separate PR to have a registered version working with the newest Manifolds.jl available sooner.

[kellertuer]

Oh, sdo I broke the tests by taking the wrong manifold :D

Yes we could merge and register this sooner I can surely do the other points (besides a news entry) also in a follow up PR, then we have this out working and I can check with Simon why his code is not working.