Alternative for: "If possible save the last selected node in the proof, to reselect it upon loading."

[wadoon]

Alternative version for #3324 using the settings instead of storing it in the proof.

Using a path encoding of the current node (list of child indexes) and a run-length encoding to keep it small.

Missing: Finding the right spot where the KeYUserProblemFile is available and the proof is loaded. The current place is unsuitable.

[wadoon]

@unp1 I now call getMediator().nonGoalChosen(node) with a valid node, but it is not selected. Where is the other place with the logic that the last node should be taken?

[wadoon]

@unp1 @mattulbrich I updated this to the latest main. The current obstacle is the lack of communication bandwidth, which prevents the provision of additional information to the UI world.

I can vaguely remember that we had a conclusion in Feb'2024 that the additional (KeY-/tool-maintained) information should be separated from \settings {}. Correct?

[codecov]

Codecov Report

❌ Patch coverage is 67.93893% with 42 lines in your changes missing coverage. Please review.
✅ Project coverage is 37.93%. Comparing base (603b2ca) to head (66b0aa4).
⚠️ Report is 1699 commits behind head on main.

Files with missing lines	Patch %	Lines
.../uka/ilkd/key/proof/io/OutputStreamProofSaver.java	25.00%	14 Missing and 1 partial ⚠️
...core/src/main/java/de/uka/ilkd/key/proof/Node.java	0.00%	12 Missing ⚠️
...n/java/de/uka/ilkd/key/settings/Configuration.java	9.09%	10 Missing ⚠️
...uka/ilkd/key/macros/scripts/ProofScriptEngine.java	0.00%	2 Missing ⚠️
.../src/main/java/de/uka/ilkd/key/nparser/KeyAst.java	90.90%	1 Missing ⚠️
...de/uka/ilkd/key/proof/init/KeYUserProblemFile.java	75.00%	0 Missing and 1 partial ⚠️
...n/java/de/uka/ilkd/key/settings/ProofSettings.java	90.00%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##               main    #3380    +/-   ##
==========================================
  Coverage     37.93%   37.93%            
- Complexity    17030    17038     +8     
==========================================
  Files          2060     2060            
  Lines        126300   126409   +109     
  Branches      21304    21324    +20     
==========================================
+ Hits          47913    47958    +45     
- Misses        72499    72560    +61     
- Partials       5888     5891     +3     

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