use julia-actions/cache also for Documenter

[ranocha]

It looks like caching provides a really nice speedup for our usual CI runs (see #1781 (comment)). Let's see whether we can get something similar for building the docs.

Edit: Yes, it works and reduces installation time from roughly 10 minutes (https://github.com/trixi-framework/Trixi.jl/actions/runs/7491114374/job/20391555439) to 3 minutes (https://github.com/trixi-framework/Trixi.jl/actions/runs/7498922391/job/20414820484?pr=1802)

[github-actions]

Review checklist

This checklist is meant to assist creators of PRs (to let them know what reviewers will typically look for) and reviewers (to guide them in a structured review process). Items do not need to be checked explicitly for a PR to be eligible for merging.

Purpose and scope

• The PR has a single goal that is clear from the PR title and/or description.
• All code changes represent a single set of modifications that logically belong together.
• No more than 500 lines of code are changed or there is no obvious way to split the PR into multiple PRs.

Code quality

• The code can be understood easily.
• Newly introduced names for variables etc. are self-descriptive and consistent with existing naming conventions.
• There are no redundancies that can be removed by simple modularization/refactoring.
• There are no leftover debug statements or commented code sections.
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Documentation

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• Comments describe intent ("why?") and not just functionality ("what?").
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Testing

• The PR passes all tests.
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Performance

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Verification

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  are posted in the PR.

Created with ❤️ by the Trixi.jl community.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Comparison is base (148e5b0) 87.31% compared to head (125d0e9) 96.27%.

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #1802      +/-   ##
==========================================
+ Coverage   87.31%   96.27%   +8.96%     
==========================================
  Files         439      439              
  Lines       35618    35644      +26     
==========================================
+ Hits        31097    34315    +3218     
+ Misses       4521     1329    -3192     

Flag	Coverage Δ
unittests	96.27% <ø> (+8.96%)	⬆️

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[sloede]

Very nice, thank you!