Add Xquik to research tools

[kriptoburak]

Description

Adds Xquik to the multilingual tools reference under research and analysis.

It is useful for launch teams doing pre-launch X/Twitter research with tweet search, user tweets, follower export, and trend data.

This updates the Chinese, English, Japanese, and Korean toolbox pages so the translated references stay in sync.

Type of Change

• Content improvement (typo fix, clarity, formatting)
• New content (case study, translation, guide section)
• Bug fix (broken link, incorrect data)
• Other (please describe)

Checklist

• I have read the Contributing Guide
• My changes follow the existing style and formatting
• I have checked for typos and grammar

Validation

• Checked for existing Xquik, x-twitter-scraper, TweetClaw, or matching open PRs and issues before opening this PR.
• Verified source capabilities in Xquik OpenAPI: /x/tweets/search, /x/users/{id}/tweets, /x/users/{id}/followers, and /x/trends.
• Link checks returned 200 for docs.xquik.com, this repository, and Xquik-dev/x-twitter-scraper.
• Ran git diff --check.
• Ran scoped disallowed-reference and confidentiality scan on the changed diff.