What actually happens
Opportunistic theft. A bag visible on a car seat, a phone left on a beach towel, a ground-floor window open overnight, a bicycle not locked. The pattern is the same one you would recognise from any small town anywhere that has a lot of visitors passing through.
The countermeasures are equally ordinary. Do not leave anything visible in a parked car, at all, ever. Lock up at night. Do not take valuables to the beach. Locals do all three without thinking about it, which is the tell.
The two things that actually hurt people
The sea. Rip currents are the real danger on this coast and they take stronger swimmers than you would expect. Some beaches are calm and swimmable, some are not, and the difference is not visible from the sand. Ask, and swim where other people are swimming.
The roads at night. Unlit, occasionally potholed, and shared with pedestrians, cyclists, dogs and the occasional horse. Anyone who has lived here a while treats driving after dark as a different activity from driving in daylight, and drives accordingly or does not drive at all.
Those two account for far more trouble among foreign residents than crime does.
What about the wildlife
Almost none of it is a threat. The list of animals on this coast that deserve genuine caution is short: the crocodiles in the estuaries, a few snakes, Africanized bees, and the mosquito that carries dengue, which is a daytime biter and breeds in the saucer under your potted plant.
Everything else, including the howler monkeys that will convince you on your first morning that something terrible is happening, is noise.
The honest framing
Costa Rica is not a place where nothing happens. It is a place where the things that happen are mostly property crimes of opportunity, and where the sensible response is the same set of habits residents already have. Ask three residents what they lock and when, and copy them.