Do plants like caffeine?

It might keep them up a bit.

Watching 2 vines growing next to each other, one getting a weekly dose of leftover coffee, I say, no. The one without the coffee is doing much better. I’d give your plants extra water for a couple weeks and don’t do that again.

It has what plants crave.

For serious, though, plants don’t have adenosyne receptors, so it’s not going to help them cram for finals.

Back in the day, decades ago in college, when I and housemates grew some “herb” on the patio, some of those plants got coffee grounds in their soil regularly and were reputed to have a special buzz when smoked. (Personally I didn’t notice a difference.)
There was no sign the plants were growing better or worse for it, though. These plants got a lot of attention and we would have noticed.

Caffeine is produced by plants to discourage insects from eating them. So plants that don’t manufacture caffeine on their own may benefit from adding caffeine to their soil (if they can tolerate it). If the caffeine is absorbed into the plant’s root and deposited into other plant parts (stems, leaves, flowers and fruit) then plant eating insects may be less inclined to eat the plant. Unfortunately for the plant, this strategy of defense doesn’t work too well on humans.