return nothing & helper functions for custom time integrators

[DanielDoehring]

Follows upon #2516 .

Also, I am bundling some helper functions to avoid duplicated code.

[github-actions]

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[codecov]

Codecov Report

❌ Patch coverage is 98.86364% with 1 line in your changes missing coverage. Please review.
⚠️ Please upload report for BASE (main@531ee91). Learn more about missing BASE report.

Files with missing lines	Patch %	Lines
src/time_integration/time_integration.jl	96.43%	1 Missing ⚠️

Additional details and impacted files

@@           Coverage Diff           @@
##             main    #2517   +/-   ##
=======================================
  Coverage        ?   96.75%           
=======================================
  Files           ?      512           
  Lines           ?    42387           
  Branches        ?        0           
=======================================
  Hits            ?    41010           
  Misses          ?     1377           
  Partials        ?        0           

Flag	Coverage Δ
unittests	96.75% <98.86%> (?)

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[bennibolm]

Looks good to me, thanks.