Make it an option upon making a seasonal character to carry over all quest progress. Practically no one is going to re-do up to 200 quests every season and you just end up with a cluttered map and a quest log from picking up random items that start that or another quest.
Having exclamation marks all over a city is annoying too.
I believe they said in stream you dont need to do it again. You can still repeat the side quests but you dont get renown for previously completed ones.
The permanent renown rewards carry over. This is skill points, max potions, max obols, and paragon points.
The one-time rewards (gold) and associated renown is still per-character, and the only parts that carry over for this are lilith altars and map revealing. This means you can still do dungeons/side quests/strongholds for renown and get those gold rewards.
Also yes they corrected the thing about HC. They were saying SC completion doesn’t carry over to HC in the original tweet but worded it badly. HC completion rewards carries over to HC S2.