Make playground.matrix.org better known

the playground is quite useful, but we don't really link to it https://github.com/search?q=repo%3Amatrix-org%2Fmatrix.org%20playground.matrix.org&type=code or https://github.com/search?q=repo%3Amatrix-org%2Fmatrix.org+docs%2Fapi&type=code

the spec also only links to it, once, and not too obviously https://github.com/matrix-org/matrix-spec/blob/6f1e64cb1271189cfa6bc310564f35d895326671/content/_index.md?plain=1#L34

Start with the repository search results for playground.matrix.org and docs/api, then compare them with the referenced Matrix specification landing-page link. Add appropriate, more visible links to the playground in the relevant documentation or website content, and confirm that readers can discover it without relying on the single existing spec link.

Written by the indexing model from the issue text.