Recommend the new REPL mode in asyncio REPL docs

[bswck]

Issue to track the agreements from #140013.

cc @kumaraditya303

Linked PRs

• gh-140569: Recommend the new REPL in the asyncio REPL docs #140570
• [3.14] gh-140569: recommend the new REPL in the asyncio REPL docs (GH-140570) #141115
• [3.13] gh-140569: recommend the new REPL in the asyncio REPL docs (GH-140570) #141116