Actually, in the US, you have a lot of time after entering a doctoral program with a bachelors to choose a specialty. The first years are advanced coursework leading to comprehensive exams. You get to look at both areas of specialization and faculty members who might advise you.
Whether a university is more interested in theoretical CS or hot topics like AI depends on the faculty and also on which of the faculty are looking for doctoral advisees.
I wouldn't be too concerned, but it would probably be good to keep your options open for the moment and project some flexibility in a statement of purpose. Saying that your current interests are in more theoretical aspects is almost certainly fine.
Note that acceptance in the US is broad based. A single thing, especially a statement of interest in theory, is likely to have very little weight compared to things like GPA, letters of recommendation, specific courses, and such.
Also note that funding is less for many theoretical fields is less because less is required. If you don't need expensive labs/equipment then there are few funding requirements. Most students in such fields are supported as teaching assistants, which provide a service to the university and are adequately funded. TCS and math are similar in this regard. Even in physics, some theoretical aspects require little if any funding beyond salary. Einstein didn't require an experimental setup to come up with special relativity. (IIRC he was terrible at experimentation.)
Don't overthink it.