Yeah definitely call the airline ASAP.
I just did a kayak search of flights to Costa Rica with plane change in Houston and it does list conditions but I see no mention whatsoever of vax requirement. I'd call this a pretty substantive omission.
A quick search of requirements for transit passengers suggests an amended health order does also catch transit passengers, but following the links I can't easily see this information. I would ask the airline to direct you to it.
There are definite doubts about the CDC being able to make orders that have force of law, not least in the wake of the judgement against the EPA which says only Congress can pass laws. However, as a transit passenger you may have difficulty asserting any rights in this regard, and at this point the airline probably are the law. However, they may have failed in their contractual obligation, in fact I would say this omission is outright misleading, and may be intentional, since they profit from selling seats people can't take up. Showing it's "your fault" may mean double-booking laws don't cover it.
There is one other angle I can think of, and that is that participants in covid vaccine trials are exempt from this requirement. There is no harm getting yourself onto the control group https://vaxcontrolgroup.com/ and then stomping your feet that it is both discriminatory and damaging to the trial to refuse you travel.
Freedom Travel Alliance (Delores Cahill) may also have an angle.
https://www.freedomtravelalliance.com/
Good luck!