Reference Issues/PRs

None

What does this implement/fix? Explain your changes.

Related to the series of examples I've been reworking.
This PR refactors the t-SNE example to demo the effect of perplexity to:

• use notebook style (see Fix notebook-style examples #22406);
• reduce boilerplate;
• add a plot to visually compare fit_transform time;
• use the default "pca" initialization in TSNE instead of the "random" init;
• use the same max_iter across datasets for a controlled comparison of fit_transform times.

AI usage disclosure

I used AI assistance for:

• Code generation (e.g., when writing an implementation or fixing a bug)
• Test/benchmark generation
• Documentation (including examples)
• Research and understanding

Any other comments?

Because of the change in the initialization and max_iter, resulting plots are slightly different from the current state of the example, but now the TSNE results are deterministic without setting a random state.