Expanded Psionics Handbook does introduce Chapter Two: Classes with
The four psionic classes, in in the order they’re presented in this chapter, are as follows.
- Psion: [...]
- Psychic Warrior: [...]
- Soulknife: [...]
- Wilder: [...]
Complete Psionic establishes that these four are “not the only psionic classes the game could feature,” but then neglects to say that the classes it presents are actually psionic classes—though “new character classes for psionic characters” maybe gets close.
So by the very strictest of RAW, the only “psionic classes” are psion, psychic warrior, soulknife, and wilder; those are the only classes that are explicitly labeled as such by an official publication.
Expanded Psionics Handbook does refer to the prestige classes in that book as “psionic prestige classes,” though it’s unclear if that counts as a “psionic class.” Likewise, precisely what erudite means in that quotation is also underdefined, and we can’t really know precisely what does or doesn’t count.
Which is precisely the situation than we have for arcane or divine, which are not defined at all. The fact that we know explicitly that psion, psychic warrior, soulknife, and wilder are psionic classes is actually an improvement over the arcane or divine side, but it’s probably not a good enough answer for handling the erudite. For that, you’ll have to ask your DM.
Personally, my ruling is that the “Exception” rule for the erudite is dumb, and should be ignored. The erudite is a variant class presented at the back of a poorly-written book, and has a lot of problems. Including it in the game necessitates some DM oversight and adaptation—part of that should be ignoring that rules, as it is a bad one. So you’ve got that going for you. On top of that, it seems to me that even if you include that rule, levels that progress erudite manifesting should count towards your erudite class level for it. So that would be in your favor, too.
All that said,
Unfortunately, I cannot more strongly recommend to any and all DMs that spell-to-power erudite needs to be banned. That option is flat-out broken, and it makes the erudite far-and-away the strongest class in the game. It is not a good addition to any game.
If you want magic spells using psionic-like mechanics, I strongly recommend Ernir’s Translation of Vancian Spellcasting to Psionic Mechanics. If you want to mix magic and psionics, play a cerebremancer—try my rework of the class if the Expanded Psionics Handbook is too much of a trap for you. But don’t play spell-to-power erudite. It is just going to break the game.