With the release of Star Trek: Picard, we've now seen Jean-Luc Picard in at least two new periods.
In which years has he been depicted so far?
Depicted means that action occurs at a particular time or an in-universe depiction (hologram, photograph, video) is shown on screen. Main TV/film canon.
Hallucinations and the like don't count ("The Inner Light", "The Battle"), but time travel does. I'm going to assume that when Q takes Picard to another time period, this really is time travel even though it's probably debatable.
In cases where the exact year is not known, a best guess or a range is acceptable.