How can a PSI increase the number of dice rolled for a skill check? For other skills the player can pick the specialized foci and bump the number of dice rolled. I don't see a similar mechanic for the psionic skills.
Typically, using psionics doesn't require a psychic skill check. Each psionic discipline is treated as a psychic “skill” (page 30), but actually using psionics involves selecting a known technique and, depending on the technique, Committing Effort (page 31). I can only find one example of a psychic skill check, and that's an opposed check when using the Cloak Powers technique (page 34).
As you've noted, none of the foci mechanically increase the number of dice rolled for psychic skill checks, probably because it's not especially useful to do so.
It's possible, but niche
The go to focus for rolling 3d6 (and dropping the lowest) is Specialist, but it forbids psychic or combat skills. The Healer focus only works for the Heal skill. These clearly don't work.
However the Sniper and Hacker foci let you roll 3d6 to do some activity without forbidding or requiring specific skills, so in you could use a psychic skill with these foci.
It's straightforward with the Sniper focus, which states:
When making a skill check for an Execution Attack or target shooting, roll 3d6 and drop the lowest die.
Normally you'd use the Shoot skill, but a Psychic employing their Telekinetic Armory technique can roll Telekinesis instead, given that the armory permits using "the Telekinesis skill as the combat skill".
On the other hand, the Hacker focus states:
When attempting to hack a database or computerized system, roll 3d6 on the skill check and drop the lowest die.
Hacking is the "the gaining of unauthorized access to data in a system or computer". Using the Program skill to force your way into a computer is the most obvious way to hack, but it's not the only viable way. For example, misleading the drunk technician to tell you the master password? That's hacking with Talk! Unfortunately, some DMs might object to this broader reading of the Hacker focus. Moreover, The psychic skills are even less applicable than Talk, but nonetheless a psychic skill could conceivably be used to hack in some niche scenarios.
It's worth noting that while the psychic techniques just happen, you might still need to roll a skill check to achieve some related feat. After all, the psychic skills exist and are meant to be used like any other:
Skill checks tell you whether or not your hero succeeds at a particular feat of expertise or natural competence. Whenever it’s uncertain whether or not your hero can manage a feat, your GM might call for a skill check.
So for example, you couldn't get that aforementioned technician drunk, so you try to establish a level-2 Telepathic Contact to read his current thoughts. The guy failed his Mental saving throw, great, but now you want to drive his thoughts towards the master password, ideally in a way that isn't suspicious. The GM calls for either a Talk or Telepathy skill check to determine whether you manage to learn the password without drawing suspicion. You choose Telepathy and roll 3d6 because you're hacking. It's niche for sure, but it's possible.