There are various mentions and use of kata throughout Judo's short history. Although typically you're not going to find a kata that resembles the long, theatrical kata that seems to be the norm now. Judo's "kata" look more like short drills, often performed with a partner. A few examples: Kime no kata (forms of decision) are essentially self-defense drills. Kyuzo Mifune developed nage waza ura no kata (throwing techniques: reverse forms) which are basically two man drills of what to do if your opponent counters your throw (counters to the counter). I myself will utilize drills that could be classified as kata for Judo footwork, fitting in, grip fighting, and if I don't have a crash pad throws like ura nage (like a backcast/suplex) can be executed in "kata" form with a heavybag. To be split hairs you could say every throw is initially learned in two-man kata form as there's little or no resistance from uke and it's performed static at first when you're learning "textbook" form. But you fairly quickly scale up the resistance and soon use it or focus on attempting it in randori.
I wouldn't have a clue where to find vids on them, if there are any videos of them. I'm shodan in Judo and I never had to perform any formal kata/s at any level for testing. Unless you count performing a "textbook" version of a throw or mat hold on uke with very little resistance.
Honestly, when I heard "Judo" and "Kata" I was quite suprised. I didn't think it was a thing that was part of the program.
ShadowJudo (think shadowboxing, but using Judo) is useful in particular for practicing footwork and fitting in for throws. But that's envisioning hordes of grapplers (or just one phantom) coming at you both gi and no gi in dynamic fashion like shadowboxing or like when you're doing mitt work, etc. It's not a set pattern like a kata. Because of the emphasis on randori (free sparring) I don't see kata as ever evolving (de-evolving?) into having much use in Judo except as a means to give someone who is injured a chance to train, for kids as a learning aid, or for the elderly/unfirm to continue training. As someone else said here on the BBF "kata keeps you kicking"
Yes, I've read many articles on the 7 Kata of Judo and Kano Sensei is quoted as advising that the practice of Kata is important for perfecting Randori
There are two principal ways of practicing Judo: Kata and Randori. Kata, which literally means "form" is practiced following a formal system of prearranged exercise, while Randori, meaning "free practice" is practiced freely. Through Kata practice, trainees learn the principles of techniques.