Resolve "Reasoning im Frontend anzeigen"

What is new and why?

Der Reasoning-Teil der Antwort wird bei Reasoning-Modellen angezeigt, damit man den "Denk"-Prozess des Modells nachvollziehen kann.

Related issues

core#17 (closed) chat#13 (closed)

Author's TODOs

• merged latest version of target branch (e.g., main or dev) into your branch
• check if SPDX identifier MPL-2.0 and Copyright-Text 2025 Land Baden-Württemberg <InnoLab@stm.bwl.de> exists in newly created and/or hasn't been deleted somehow in existing files
• adapted the readme
• Revised/new code parts have no # noqa directives
• Optional: Changelog adapted (further information)

Reviewer's TODOs

• Check if the Author did their checks well enough
• Tried out if the cause of the issue is solved as intended
• Check that code with old # noqa directives were revised
• Check that no new # noqa directives are included
• Optional: Changelog adapted (further information)

To keep in mind

• pre-commit used
• added logging output were necessary
• added/adjusted Errorhandling to avoid unwanted crashes and make proper debugging and testing possible
• Changelog has to be adapted before merging, at latest in the f13::inAbnahme step

Closes #18 (closed)