docs: fix grammar errors and typos in README files

[syukawa-gh]

Fixes various grammar errors and typos in README files:

• "featuer" → "feature" (cx-api)
• "it's" → "its" (possessive)
• "allows to" → "allows you to"
• "the a stage" → "a stage" (apigateway)

Consolidates the following closed PRs into a single review:

• docs(cx-api): fix "featuer" typo to "feature" in README #37436, docs: fix "it's" to "its" (possessive) in README files #37437, docs: fix "allows to" grammar in README files #37438, docs(apigateway): fix "the a stage" to "a stage" in README #37439

All changes are documentation-only (README files). No code behavior changes.