fix(Latex): add latex_cache directory to resolve LaTeX compilation errors. Fixes #2390

[mathsvisualization]

Fixes #2390

Motivation

LaTeX compilation in Manim was failing due to missing directory configuration for cached compilation results.
By adding a dedicated latex_cache directory, we can avoid repeated compilation and resolve errors caused by missing paths.

This improves both performance (fewer recompilations) and reliability (LaTeX renders without errors).

Proposed changes

• Added a new latex_cache entry in default_config.yml for storing cached LaTeX compilation results.
• Updated tex_file_writing.py to use the latex_cache directory.
• Ensured that LaTeX intermediate files are properly stored and reused.

Test

To test the changes:

1. Run any scene that uses Tex or MathTex.
2. Verify that LaTeX compiles without errors.
3. Check that cached files are stored in the latex_cache directory.
4. Re-run the same scene and confirm that compilation is faster (files are reused).

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✅ This PR fixes the LaTeX compilation error and introduces a caching mechanism for more efficient rendering.

Result

Before

After