[webdriver] Reuse the HTTP connection to the WebDriver remote end (#47085)
HTTPWireProtocol has an internal flag _last_request_is_blocked to
tell if the underlying HTTP connection is unusable and should be thrown
away (see #21889). However, the transport sets the flag too early, which
has the effect of transparently closing and reopening the connection
before every request.
This is wasteful and appears to sometimes exhaust the host machine's
usable ports in long test runs (https://crbug.com/343720396). Set the
flag after it's checked to avoid unnecessary connection closures.