Firstly, I would like to point out that, when we talk about electrophiles (E) and nucleophiles (Nu), we may be calling the entire molecule an electrophile or a nucleophile, but in reality we are referring to a single atom or functional group that serves as the E/Nu. For example, when we call hydroxide (OH-) a nucleophile, we really mean that the oxygen anion is nucleophilic.
Now for hydronium. It should be noted that there are no 2p orbitals on the oxygen atom; it is sp3 hybridized. Given the positive charge on oxygen, it is already electron-deficient, meaning that it is highly unfavorable to lose more electron density by sharing it with another atom through a bond (as it would do if the oxygen acted as a nucleophile).
Instead, one off the hydrogen atoms acts as an electrophile. Once again, the positively-charged oxygen atom is electron-hungry, weakening the H-O bond and making the σ* orbital easier to donate electron density into. As a result, one of the hydrogen atoms of hydronium is quite easy to strip off, giving it its strong acidity (pKa~ -1.74). Since no other parts of hydronium react with other species, the only reactive component is the hydrogen atom, which serves as an electrophile and gives hydronium its categorization as an electrophile. Below is an arrow-pushing mechanism depicting the deprotonation of hydronium.
*Note that the oxygen of α-Methylbenzyl alcohol is acting as the nucleophile to attack a hydrogen atom of hydronium, the electrophile.