I also very much recommend Chris Marker's documentary on Tarkovsky, One Day in the Life of Andrei Arsenevitch [1][2]. Germane to this thread, he compares aspects of his films to Kurosawa in parts. Marker is also an incredible singular filmmaker, and the documentary is more of a love letter to Tarkovsky while he's on his deathbed. If you enjoy this, then oh do I envy you getting to go down the Marker rabbit hole and watching Sans Soleil and La Jetée for the first time.
[1] English with Turkish subtitles: https://www.youtube.com/watch?app=desktop&v=35lETmPDypI
[2] French https://www.youtube.com/watch?v=_M56i90Q1-Y
I think 2001 is a movie making masterclass in itself.
There are substantial differences in the tone and even the character names.
I still like Tarkovsky's version best, even though Lem was not a fan.
Yes, late Tarkovsky is great too, but it's not really quite cinema at that point. "Rublev" is The Movie in Tarkovsky's filmography.
It's also probably one of the best medieval films there is, regardless of the genre, "7th Seal" to "Kingdom of Heaven".
Another great, often overlooked movie is his very first one - "Ivan's Childhood". You can see him still begin somewhat cautious there, but the movie is as poignant as they get. It was created by one of the best artists of the generation as he watched the dawn of the 60s era as a member of the society for which World War 2 and Red Terror are yet to become "yesterday".