Conjecture on Fano planes in non-classical unitals of even order

Let $q$ be even, let ${\mathcal U}$ be a non-classical unital in ${\operatorname{PG}}(2,q^2)$, and let a Fano plane mean an embedded projective plane of order $2$.

Fano-plane conjecture. Every non-classical unital ${\mathcal U}$ in ${\operatorname{PG}}(2,q^2)$ contains a Fano plane if $q\geq 4$.

The paper proves the existence of Fano planes in orthogonal Buekenhout--Metz unitals of even order, providing evidence for this broader claim about non-classical unitals. The supplied material gives no resolution of the conjecture in general.