logtail: remove unncessary response read

Effectively reverts #249, since the server side was fixed (with #251?)
to send a 200 OK/content-length 0 response.

Signed-off-by: Mihai Parparita <mihai@tailscale.com>
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Internal Server Error - Gitea: Git with a cup of tea
500 Internal Server Error

Gitea Version: 1.28.0+dev-477-g8b6ad49a5f