Characteristic-two regularity upper-bound conjecture

Assume that ${\Bbbk}$ has characteristic $2$, let $R={\Bbbk}[x,y,a,b]$, set $Q=(x^3,y^3)$ and $f=xya-(x^2+y^2)b$, and let $n=2^s$ for some $s\in\mathbb N$. Characteristic-two upper-bound conjecture. There exists $\epsilon>0$ such that

$$\operatorname{reg}(Q^n+(f^k))\leq(5-\epsilon)n+k$$

for every integer $k$ with $1\leq k\leq n$. The source states that this conjectural bound would imply the missing lower-asymptotic estimate needed to establish nonexistence of the symbolic-power asymptotic regularity limit.