I think it ended in the late 2010s, when streaming took over:
Over the 2000s and early 2010s, writers were perfecting the style first experimented with by the great shows of the 90s and earlier, where seasons were mostly episodic but led into serial plot. Several of those early ones have been mentioned in these comments, and often alternated episodic and serial, while the later ones were figuring out how to mix the overarching plot into the episodic ones, advancing it slowly as something extra so viewers could miss one or two episodes without getting lost. Then at the midseason and season finales it'd be a big event for the larger arcs, bringing it all together.
Streaming no longer had to worry about viewers missing an episode, so all the episodic filler started getting dropped in favor of streamlining the overarching plots. Unfortunately, what we lost along with it was things that were less filler and more character and world building. Getting to know the characters through action instead of summarizing it with narration, making the setting feel more real, laying out events and actions in a more natural way instead of it feeling contrived.
For example: https://www.youtube.com/watch?v=Fjd9RgRUQDY
The backstory that makes this scene work so well was almost all in those episodic character and worldbuilding episodes we don't really get nowadays. We actually watched these characters develop and grow and change over years before this scene. I don't really think modern TV in its serial format could have a scene with as much impact - all that "filler" makes them feel like three dimensional people rather than plot devices.