I don't see why this wouldn't be possible. What driver are you using? I'll assume "GE Smart Fan Control," but any fan (or even dimmer) driver should work. There isn't a built-in way to go precisely "up" or "down" based on the current speed; the closest you can get there is cycleSpeed, which will step up to the next supported speed and wrap around back to the lowest after it reaches the top. What you'll have to do to work around that if you want to go only up or down is set the level manually using setLevel, just like a dimmer. (Alas, Hubitat doesn't have something like a "next higher speed" or "next lower speed" you can just run, which would make this a lot cleaner.)
I'd recommend trying all the speeds your device supports and watching what the percentage is on the device page, but based on this post, I'll assume it's 25%, 50%, and 75%. Assuming that's correct, an easy way out would be to map the up and down buttons to increase or decrease the speed by 25%. This may cause issues with some edge cases, but I'm not familiar enough with this particular device to know. What I mean is that when on low, decreasing 25% by 25% may take it down to 0%, which usually turns off the device. Increasing 75% by 25% may take it up to 100% (no change since they're both high but would require an extra press to get it back down to 50%/medium), but that's generally not a value supported by most Z-Wave devices, so it may either fail or set you at a 99% cap (neither of which would change anything, and the latter is unlikely to cause any problem except the former).
To get it to to exactly what you want, you could create a rule. How did you set up what you already have? I'd use a "Button Device" trigger capability in Rule Machine, though Button Controller alone (this trigger in RM basically gives you a same interface with a bit more power) should also be able to handle this. In your actions for the up/down buttons, you can check the current level and adjust accordingly if needed (e.g., for the up button, actions that effectively do: if current level >= 33% then set to medium; else if current level >= 66% then set to high). This is a bit more work for only marginal benefit over the basic solution proposed above, but it's certainly possible if you figure out what percent ranges your fan uses. I'd be happy to help you write such a rule if you're unfamiliar.
