Confusion regarding SameSite changes with Chrome
as mentioned here https://web.dev/samesite-cookies-explained/:
If the user is on www.web.dev and requests an image from static.web.dev then that is a same-site request.
Same as your first case:
Site: https://a.a.comAPI: https://b.a.comSo the browser considers your first request as a same-site request and cookies won't be removed, but the second one is a cross-site request and cookies without samesite attribute will be removed.