Interconnected, for sure.
For a time there they were actually doing a pretty good job with it too. Nearly every game from OoT onward actually felt like it related to a previous entry quite directly, with the entirety of the Adult timeline being a perfect example.
The only ones that do a poor job in that timeframe are, surprise surprise, the ones that were developed by Capcom. I’m not sure if they had any say on the story aspect, but given how I don’t think they did a particularly good job on the rest of the games, I wouldn’t be surprised if that major disconnect stemmed from them. Even TP, as shoehorned as nearly every plot element is, makes it abundantly clear that it’s plot is an evolution of the child portion of OoT.
Then you get to BotW, where they throw all plot consistency out the window. The franchise effectively had 3 separate story’s going on, each had some sort of world progression and an actual effort put in making the world of Hyrule seem dynamic, but the 10000 year gap just kinda renders all of it pointless. To be fair I think that TFH already felt completely disconnected from it’s own predecessor despite being a direct sequel, but that’s just a tiny little multiplayer game that nobody ever talks about. Outside of a few vague references, the only time BotW specifically relates itself to a previous title is when Fi kinda sorta shows up and becomes a minor plot point in both Link and Zeldas arc.