Most of the game is solo-friendly. Some things are very difficult to solo, but if you get really good at the combat system it’s still possible.
Coordinated end game party stuff isn’t my bag so much, so I’m not sure about soloing it. There are a lot of different things you can do with different names that all amount to dungeon/raid style content. The things actually called “dungeons” are all from the original game and are really old at this point. The newer 5 man dungeons are called “Fractals”, and there are also 10 man raids, and 10 man boss only encounters called “Strike Missions” (basically a single raid boss with no dungeon around it).