In the case of the Psi Knight, the psionic features are "spells", and therefore are "magic".
In 3e and 4e, psionics is explicitly a form of magic. In other words, the position of WotC has always been psionics=magic. WotC objects to certain TSR traditions.
That said, 5e core books avoid the topic of psionics entirely − except for a brief note in the Monster Manual. This is the only 5e core rules with regard to psionics.
MM 10.
"
PSIONICS
A monster that casts spells using only the power of its mind has the
psionics tag added to its
Spellcasting or
Innate Spellcasting special trait. This tag carries no special rules of its own, but other parts of the game might refer to it. A monster that has this tag typically doesn't require any components to cast its spells.
"
That is all 5e has to say about psionics.
Psionics = "spellcasting" "using the power of ones mind"
Normally, psionic spells lack any kind of spell component, whether material, somatic, or verbal.
Tashas is dejure optional but defacto core. Therefore, what it says about psionics is of interest for trying to divinate the intentions of the 5e designers.
I have to admit, Tashas seems to resort to "weasel wording" carefully ambiguous statements, in order to avoid committing to whether psionics is magic or not.
I feel
@Steampunkette goes beyond what the text actually says, but her(?) main interpretation that ... psionics is a nonmagical source that can cause magical effects ... seems reasonable to me. One can oppositely argue that psionics is a magical source, but the 5e wording remains ambiguous enough that it being a nonmagical source is also possible.
If we entertain that psionics is a nonmagical source, we nevertheless have a situation where the psionic effects are magical. So far, 5e in the Monster Manual and in Tashas makes explicit that psionic effects are "spells", and as spells an antimagic field can suppress or nullify them.
I dont mind the term "Weave", because it can refer to the "tapestry of fate", or the "interconnectedness of all beings", or the "synchronicity" as an acausal cause aligning with psychological archetypes. The term Weave remains useful enough whether one is in a Forgotten Realms setting or not.
Perhaps psionics is the inherent capacity of a nonmagical mind to manipulate the magical Weave. The Weave itself is understood as a kind of primordial "will". It seems that the free will of the minds of beings inherently participate in this will.
In sum, whether a "mind" is magical or not, all psionic effects are inherently magical spells, involving the Weave.