Move Query DSL tutorial to Query languages

[lcawl]

This PR must be merged after elastic/elasticsearch#133362

It removes the query DSL API quickstart from docs-content since the other PR moves it to the Elasticsearch repo and a new section of the documentation.

[github-actions]

🔍 Preview links for changed docs

• solutions/search/api-quickstarts.md
• solutions/search/esql-search-tutorial.md
• solutions/search/full-text.md
• solutions/search/get-started/index-basics.md

[leemthompo]

Hey @lcawl I would be adamant that we not put this in Explore & Analyze, as you mentioned we've discussed this at lot with Florent and like the ES|QL section, the bulk of the rest of the query language stuff should also eventually be re-homed back to the elasticsearch repo. Stuff is too scattered today.

So I'd say either move this somewhere else in the solutions/use case or into the ES repo :)

[lcawl]

So I'd say either move this somewhere else in the solutions/use case or into the ES repo :)

Yeah, I found #1808 and elastic/elasticsearch#133301 only after doing this quick draft so I'll follow the pattern of we're moving to with ES|QL and close this PR.

[szabosteve]

LGTM, thank you!

[leemthompo]

Setting this to merge to minimize risks of SEO duplication issues :)