I never once heard nor thought the matrix sequels were planned from the beginning. The first movie is completely self-contained. The feel of the sequels is of someone stretching out a completed story, because of the money made from the first one, not anything pre-planned from the beginning, and they also feel like 1 movie that was made artificially into 2 to get more box office money.
I've always suspected that the Matrix trilogy was pre-planned in the same sense as Star Wars had a planned 9 episode arc as George Lucas always claimed.
That is, sure, they had a general sense of the surrounding world and events and what might happen next. But when someone actually said "here's an unfathomably large amount of money, please make these movies" they had to actually come up with all the concrete details and probably moved a lot of things around while doing so.
I seem to recall from the time that the Wachowskis originally planned the Matrix storyline as a trilogy, but then they were forced into making a single movie, and so took all the fantastic parts of the whole trilogy and crammed it into one movie.
Then they had to turn it into a trilogy again, and, well, it's hard to unscramble an egg.
Lucas had a script, and A New Hope ended up being the middle of it. He was all over the place. He wanted an Obi-Wan story, a Wookie movie, etc. Empire wasn’t the original sequel, but it got so big they double downed and then he just rehashed the first plot for RotJ (in the original script the Wookies helped destroy the first Death Star, but Ewoks were better for Toys R Us).
The prequel trilogy then just made it “Anakin’s story” and in 2008 he was saying he was done and there was no thereafter. Given how bad those were, he would probably have not done much better than Disney for the last three.