Is precognition the only form of psi?

I don't think that's so.

The problem is that PSI is often expressed in terms of acquisition of factual information. That is a flawed and inadequate description, which leads to absurd theories.

I've already described in other threads how reincarnation is not related to factual information, it is about a state of being. Hence super-psi whether in the form of precognition or not, would fail to explain reincarnation.

In more everyday experiences of what might be considered telepathic contact, again it is very often not facts which are transmitted, but a sharing of strong emotions, such as love or anger or distress, and also often (but not always) accompanied by a sense of the identity of the other party. These things are difficult, if not unethical, to test in a laboratory setting, hence tend to be ignored by researchers conducting tests into psi. When I say sharing, this doesn't mean having prior knowledge of some emotion which will be experienced later, that would be an absurd and incorrect description.

The reason I think May's theory is difficult to falsify is that - if I understand correctly - the precognition can be "telepathic precognition" (in which the subject never perceives the target information) or even "clairvoyant precognition" (in which no one ever perceives it but it's stored electronically). Obviously unless the information is stored in some form it's difficult to verify that it has been perceived by the subject. Perhaps it could be done cryptographically. But I still don't understand the point of suggesting that everything can be explained in terms of precognition, when precognition is so broadly defined. If it were precognition of something later experienced by the subject, then I could see the point. But there are already experimental data that tend to falsify that idea.