The word geuomai (γεύομαι Strong’s G1089) occurs 15x in the TR and is translated 12x as “taste” and 3x as “eat” in the KJV. To better understand its meaning, I examined the other Greek words that convey the idea of eating in the NT. According to Vines Expository Dictionary, there are nine verbs that can mean "to eat." Six, including geuomai, are listed below, along with a quick summary of their gloss/usage. The words are further sorted according to the frequency with which they occur in the NT:
More common:
esthio &
phago –
to eat, used of ordinary food and drink; metaph. to devour
katesthio
– to consume by eating; metaphor. to devour, to squander
Less common:
geuomai –
to taste, to eat; metaph. to experience
trogo –
to gnaw, crunch, used figuratively of the flesh of Christ
korennymi
– to eat enough, to be satiated
While there is a choice of words for the act of eating, geuomai is the only verb cited by Vines as having the meaning of “to taste.” It is also the only word that, when used metaphorically, means “to experience.” Even where geuomai is translated as “eat” (Act 10:10, 20:11, 23:14 KJV), the contexts do not indicate the complete devouring of something or the partaking of a full meal (cf. esthio, phago, and katesthio). Neither is there the suggestion of a protracted activity (cf. trogo) nor the kind of eating that satiates (cf. korennymi).
The OP asks, “Can ‘tasting’ be shallow and incomplete if as in 1 Peter 2:3 it does not mean ingestion but is seen as a preliminary to ingestion?” Based on the above discussion and on the contexts in which geuomai is used, I think the difference between geuomai and the other types of eating actions is less about the depth than the scale of the experience, whether we are speaking of food/drink or something else. A taste may consist of a single bite or a tiny sip yet still be sufficient to provide a real and direct knowledge of something (cf. Heb 2:9).
Tasting is therefore viewed as more than just a preliminary to ingestion. As the OP notes, “To tell the difference between water and wine only a taste in the mouth would be decisive.” In 1 Peter 2-3, one could argue that only those who have tasted the goodness of the Lord would know to long for what is pure. More importantly, the knowledge gained through tasting can serve as the basis for both choice (cf. Mt 27:34) and accountability (cf. Heb 6:4-6).