I recently started playing Urban Terror after seeing it posted here. The gunplay, weapon design, and map design all remind me a lot of CS as well (I never played Quake 3 so I have no reference point there).
That’s exactly where CS actually came from. The Q2 mod, Action Quake2, where every round starts with “Lights, Camera, Action”.
The developer of action quake 2, Gooseman, went on to create CS as a mod for half-life.
Urban terror is the Q3 port of action quake 2.
AQ2 still has a small community of players. I get on occasionally for the nostalgia hit. I’ve never found an FPS that’s as fast paced and difficult to master (movement primarily).
Interesting bit of history. Didn't play Action Quake 2, but had great fun playing The Specialists, which I believe was also inspired by Action Quake 2.