I really want to know the context and scope of classic love you mentioned, but for now, I'll comment according to the panels you posted.
If it's a classic love drama like what you shown in the panels, and synopsis of your story, no. It is not out of date, at least in my country (Indonesia). I tried to release my novel in Indonesian online platform and all I see is classic love drama novels, and the one with high school love vibes fills a lot the list.
International platforms have broader genre, maybe this is why you asked this. More people adding spices (psychological issues, more adult stories, etc). More genre also present and have prospect, like how my fantasy series has a lot of reader here but almost none in local online platform of mine so far.
If the scope is comic, also not in my country. Webtoons about school life (including love life), daily life of adults, are those which gets famous because they are relatable.
This is what I seen. Correct me if I am wrong, though.