Fix various UI bugs

[FliegendeWurst]

I recommend reviewing this PR commit-by-commit. Most of the bugs were found using the new UI testing facility (3d73e59).

Fixes #3228, #3227, #3215, #1648, #1652 (comment), #1526, #1117 and task 1+4 of #3214

[codecov]

Codecov Report

Merging #3216 (cbd6e0c) into KeY-2.12.0 (c628a78) will increase coverage by 0.03%.
Report is 12 commits behind head on KeY-2.12.0.
The diff coverage is 76.59%.

@@               Coverage Diff                @@
##             KeY-2.12.0    #3216      +/-   ##
================================================
+ Coverage         37.72%   37.76%   +0.03%     
- Complexity        16851    16872      +21     
================================================
  Files              2054     2053       -1     
  Lines            126475   126494      +19     
  Branches          21255    21258       +3     
================================================
+ Hits              47711    47766      +55     
+ Misses            72920    72884      -36     
  Partials           5844     5844              

Files Changed	Coverage Δ
.../ilkd/key/prover/impl/DefaultTaskFinishedInfo.java	26.66% <0.00%> (-1.91%)	⬇️
...n/java/de/uka/ilkd/key/settings/ProofSettings.java	73.07% <22.22%> (-2.18%)	⬇️
...ka/ilkd/key/proof/reference/ReferenceSearcher.java	83.56% <90.00%> (+4.99%)	⬆️
...ore/src/main/java/de/uka/ilkd/key/proof/Proof.java	77.67% <100.00%> (+0.47%)	⬆️
...de/uka/ilkd/key/proof/init/KeYUserProblemFile.java	74.35% <100.00%> (+0.33%)	⬆️
...ore/src/main/java/de/uka/ilkd/key/rule/Taclet.java	77.96% <100.00%> (+0.41%)	⬆️
...in/java/de/uka/ilkd/key/settings/ViewSettings.java	38.34% <100.00%> (+1.42%)	⬆️

... and 12 files with indirect coverage changes

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[mattulbrich]

#3214 could be of interest here too.

[github-actions]

Thank you for your contribution.

The test artifacts are available on Artiweb.
The newest artifact is here.