You forgot the main quests.
As for the gigs, yeah, there's a LOT of them in this game (half of all side quests, if I'm not mistaken) and context was indeed mostly provided through the text, but I still had fun doing them. What they lack the most compared to the best mini sidequests from TW3 and what I believe it makes them less memorable in the eyes of the many is the emotional impact (there's no equivalent of Little Red, Black Pearl, Blood Ties, Equine Phantoms, etc...)
I didn't forget - the main quest is one of the 5 chains I mentioned, of course
But no, I don't think it's just the lack of emotional impact, it was the lack of context that made me feel like the quests in Cyberpunk were wasting my time, for the most part.
As an example, monster contracts in TW3 were not so different from cyberpsycho hunts in CP, but the difference for me was that a Cyberpsycho fight was built up by... a short, impersonal, non-interactive lore-dump. In TW3, you had to go talk to a person, get information, yes maybe even some emotional stakes, understand the impact your action is going to have on the world, and then you have the fight - after some investigation that fed into the preparation mechanic.
It was a similar situation for all the side gigs. I think CP missions had more complex design in terms of gameplay than the quests in TW3, but the lack of context made it feel like I was just following quest markers and checking items off a list. Better games, TW3 included, hide that inescapable fact with more effort and variety put into presenting the story and context of the quest.
So, to sort of bring this back on topic... I hope CDPR and Pawel Sasko are able to identify and address the issues in CP's quest design so that future titles can benefit.