Museums nowadays introduce some forms of edutainment, for example children play rooms. So the botanical gardens could follow, too.
Botanical gardens might be a place to put those large screen displays which infected aquaterrarium Aquatis in Lausanne. A large presentation screen is flat, so could be easily retrofitted in an existing greenhouse, which is usually cramped. Humidity could be a problem, but the screen at Aquatis survives it.
I imagine, for example, that a greenhouse could have a large screen set at the back. It would show a fake background of the natural habitat. Then a guy like David Attenborough would appear on the screen, point at the real plant specimens in the front, and tell 'this is .... and is special because...'. Perhaps small windows could popup, showing things like diagrams of the structure of the plant, distribution maps, a film about hummingbirds pollinating plants, a film about cycads or tree ferns showing that dinosaurs ate very similar plants in the Mesozoic, faraway people cultivating or eating this plant etc. Perhaps care should be taken that these displays don't create an anoying background noise murmur.
However, this would require separate donations, because the budget of an average botanical garden is usually very low.