The practical answer is usually two fixtures doing two jobs, and there is no shame in it.
The light that came with a terrarium kit is generally sized to make the tank viewable and to provide whatever the animal needs. That is a legitimate job and it is not the same job as growing plants at the bottom of a tall enclosure.
What to look for in a plant light for this:
A fixture that states output for growing, rather than one sold on wattage or brightness alone. The specification you want is about photon output in the useful range.
Enough to reach the substrate. In a tall tank, that means a stronger fixture than the same tank would need if it were short, and it is worth choosing on that basis rather than on tank volume.
A sensible photoperiod, in the region of ten to twelve hours on a timer. Longer does not compensate for too little intensity, plants need a threshold, not a total, and extending a dim day mostly just grows algae.
And check the animal's requirements are still met and not exceeded. A brighter tank changes basking behaviour and the amount of cover a shade-dwelling species wants. More plant cover, which you are about to get, usually helps with that: the two things solve each other once the plants actually grow.