Are there any builds that are actually fun and engaging to play?

You should check any channeling skills, they often offer differend kind of gameplay - flameblast, incinerate, scourge arrow and others, you can check on wiki.
Also any type of vaal skill-based builds, not sure some of them are still there, but previously i have seen some vaal blight/EQ builds, they kinda need proper managing of your flasks/cooldowns.

Many 1 button builds can become more technical by simply removing a little gem known as Cast When Damage Taken (CWDT). Add a guard skill if there isn’t one. Throw a Warcry in there. Actually cast a Curse yourself. Use a secondary skill with a duration. Many builds become stronger if you remove the automation mechanic(s). Other times the time it takes to cast is inferior to an automation.

Ooh, just remembered my least favorite build ever: Spectral Blades. Those get more obnoxious than technical imo, but it may fit your mold.