Dehydration of primary alcohol with a cyclobutadiene substituent
You have misinterpreted what Wikipedia has said. I'd put whole quote here:

Cyclobutadiene is an organic compound with the formula $\ce{C4H4}$. It is very reactive owing to its tendency to dimerize. Although the parent compound has not been isolated, some substituted derivatives are robust and a single molecule of cyclobutadiene is quite stable. Since the compound degrades by a bimolecular process, the species can be observed by matrix isolation techniques at temperatures below $\pu{35 K}$. It is thought to adopt a rectangular structure.

These somewhat stable cyclobutadiene derivatives are not just derivatives with a simple alkyl substituent. They are with bulky substituents, e.g., tetrakis(tert-butyl)cyclobutadiene. Therefore it is safe to assume that given compound (2-cyclobutadienylethanol) does not exist. However, as Aniruddha Deb has said, we can treat it like it is existing only for this theoretical question (we don't have other choice):
Since it is a primary alcohol it can't undergo usual $\mathrm{E1}$ elimination with an acid. The $\mathrm{E1}$ pathway through formation of a primary carbocation is not the most likely pathway here, because primary carbocations are extremely unstable. Therefore, more likely, this reaction undergoes through an $\mathrm{E2}$ mechanism where the transition state should be lower in energy. Accordingly the protonation of the alcohol group to give the good leaving group $\ce{-OH2+}$:

And then, a weak base (which could be either $\ce{H2O}$ or $\ce{H2PO4-}$, or even another molecule of the alcohol) could abstract $\beta-\ce{H}$ from nearby $\beta$-$\ce{CH2}$ group, leading to give the conjugated alkene with cyclobutadienyl group (vinylcyclobutadiene):

We really don't know how stable vinylcyclobutadiene is, but it should be more stable than original alcohol since it has additional resonance contribution with external vinyl group. This compound can undergoes either Diels-Alder or Cope rearrangement to give a bicyclo[2.2.0]hex-1,5-diene derivative. This derivative should be unstable due to severe strain, and expected to rearrange to Dewar benzene derivative, which then rearrange to benzene upon heating (Ref.1).
Reference:

L. Watts, J. D. Fitzpatrick, R. Pettit, &quot;Cyclobutadiene,&quot; J. Am. Chem. Soc. 1965, 87(14), 3253–3254 (https://doi.org/10.1021/ja01092a049).