Remove unused variables `save_time_series_file`

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.
[ ] The code adheres to our conventions and style guide, and to the Julia guidelines.

Documentation

[ ] New functions and types are documented with a docstring or top-level comment.
[ ] Relevant publications are referenced in docstrings (see example for formatting).
[ ] Inline comments are used to document longer or unusual code sections.
[ ] Comments describe intent ("why?") and not just functionality ("what?").
[ ] If the PR introduces a significant change or new feature, it is documented in NEWS.md.

Testing

[ ] The PR passes all tests.
[ ] New or modified lines of code are covered by tests.
[ ] New or modified tests run in less then 10 seconds.

Performance

[ ] There are no type instabilities or memory allocations in performance-critical parts.
[ ] If the PR intent is to improve performance, before/after time measurements are posted in the PR.

Verification

[ ] The correctness of the code was verified using appropriate tests.
[ ] If new equations/methods are added, a convergence test has been run and the results are posted in the PR.

Created with :heart: by the Trixi.jl community.

Codecov Report

All modified and coverable lines are covered by tests :white_check_mark:

Project coverage is 96.08%. Comparing base (37bbe15) to head (cdfd6eb).

Additional details and impacted files

```diff @@ Coverage Diff @@ ## main #1928 +/- ## ========================================== - Coverage 96.08% 96.08% -0.00% ========================================== Files 450 450 Lines 36215 36215 ========================================== - Hits 34797 34796 -1 - Misses 1418 1419 +1 ``` | [Flag](https://app.codecov.io/gh/trixi-framework/Trixi.jl/pull/1928/flags?src=pr&el=flags&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=trixi-framework) | Coverage Δ | | |---|---|---| | [unittests](https://app.codecov.io/gh/trixi-framework/Trixi.jl/pull/1928/flags?src=pr&el=flag&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=trixi-framework) | `96.08% <100.00%> (-<0.01%)` | :arrow_down: | Flags with carried forward coverage won't be shown. [Click here](https://docs.codecov.io/docs/carryforward-flags?utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=trixi-framework#carryforward-flags-in-the-pull-request-comment) to find out more.

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trixi-framework / Trixi.jl