What is the importance of food in Trika Shaivism?

In short: very little. We believe there is nothing metaphysical that makes certain kinds of food “pure” and other kinds of “impure”. There is only what is healthy or not healthy for the physical body, which is different for every single Jiva. The type of food you eat extremely little impact on your sadhana, it only matters insofar as the physical body is healthy enough to continue doing sadhana.

In terms of the subtle body, which is the real place where spiritual transformation takes place, the type food you eat has absolutely no impact on it. So again, it only matters for the physical body which means certain foods will be better suited to each particular individual. Thus, calling certain kinds of food “pure” and others “impure” in a spiritual context is a completely made up concept. It is equally as absurd as the belief in caste by birth.

Abhinavagupta has this to say about it in his Tantrasara:

“one should not weary oneself with distinctions of what should and should not be eaten, what is pure and impure, and so on; for such distinctions are in reality only mental constructs, they are not qualities that inhere in those things themselves—such is taught in the sacred Scripture of the East (the Mālinī-vijayottara-tantra) and other sources.

For ‘purity’ is not intrinsic to a thing the way blueness is, because the very same thing may be declared as impure in another context, as in the case of giving a charitable donation when one has been initiated [for a Vedic sacrifice, which is disallowed by the Veda].

If it be argued that it really is impure for him in that context because of the applicable Vedic injunction, then the same applies in the case of other, non-Vedic injunctions. If it be argued that the non-Vedic injunction is false & unreal because it is overridden by the Veda, we will say “No, the capacity to supersede belongs to Śiva’s injunctions alone, as established by reason and countless scriptures such as the Sarvajñānottara.”

Therefore, it is established that whatever restriction, whether injunction or prohibition, that is taught in the Vedic texts, or even in the treatises of the Śaiva Siddhānta, the Bhairava-tantras, the Kula system, and so on, is entirely powerless on this level of practice. This is exactly what is taught in the sacred Scripture of the East and other sources; it may be investigated in more detail in my Tantraloka”

we find it again, wonderfully said in the Vijnana Bhairava Tantra:

“That which people of little understanding consider ‘purity’ is impurity in the teachings of Śiva. [In truth,] there is neither purity nor impurity. Therefore, be free of such mental constructs, and be happy. || 123”

And again in the Svabodhodaya-mañjarī:

“Everyday behavior is formed by mental constructs such as universal categories like caste etc. and so is based on the mind. But these categories do not actually exist. By realizing this, [the yogin] will attain tranquillity (śama).”

Thus it is the firm position in the teachings of the Trika that there is no metaphysical reality to such concepts as “pure” and “impure” outside the mental projections of the Jiva.