Fix closing the body for HTTP requests (#11842)

[dbussink]

One of the easy things to miss that can cause resource leaks is not closing a response body for an HTTP request.

There's a linter available to make it easier to catch this, so this enables that linter and fixes all the cases reported.

This is almost all test cases, except for one production code path case in the throttler.

Backport of #11842

Checklist

• "Backport to:" labels have been added if this change should be back-ported
• Tests were added or are not required
• Documentation was added or is not required

[vitess-bot]

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