Room for clarification and flow improvements in asyncio HOWTO

[anordin95]

Documentation

There are a few spots that I think could do with minor clarifications or flow improvements.

Linked PRs

• gh-138072: Small clarifications and phrasing improvements to asyncio HOWTO #138073
• gh-138072: Fix typos and grammatical errors and improve clarity in asyncio howto document #138895
• [3.14] gh-138072: Fix typos and grammatical errors and improve clarity in asyncio howto document (GH-138895) #140091
• [3.13] gh-138072: Fix typos and grammatical errors and improve clarity in asyncio howto document (GH-138895) #140092