Displaybreak for algorithms

I have the following problem. I have a relatively long pseudocode, and when I have text before it, either 1) there is a lot of white space, or 2) the text on the previous page is stretched out, or the line spacing is very large. Now I wanted to ask if it is possible to distribute the pseudocode dynamically on both pages, similar to equation with \allowdisplaybreak{}. This is my MWE, unfortunately I could only reproduce 1).

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage{algorithm}
\usepackage[noend]{algorithmic}
\usepackage[linesnumbered,ruled,vlined]{algorithm2e}

\begin{document}

\begin{algorithm}[H]
\footnotesize
\caption{Dynamic Task Assignment}
\label{algo:task_assign}
\KwIn{$\mathcal{J}^{\text{High}}, \mathcal{J}^{\text{Low}}, \mathcal{W}, \mathcal{S}^{\text{Time}}, R_j^{\text{Start}}, R_j^{\text{Dur}}, BW, \underline{BW}, C_{ws}, \alpha^{\text{Eff}}_{type}, optimization~params$}
\KwOut{$z_{jws}^{\text{High}}, u_{js}^{\text{High}}, COST_j^{\text{High}}$}

\textbf{Step 0: Reserve resources for priority jobs}\\
\ForEach{$j \in \mathcal{J}^{\text{High}}$}{
    deadline $\leftarrow R_j^{\text{Start}}$; \\
    \If{$\exists w \in \mathcal{W}$ with $C_{ws} > 0$ on deadline}{
        Reserve one unit: $C_{ws} \leftarrow C_{ws} - 1$\;
    }
    \Else{
        \Return{Infeasible}
    }
}
\textbf{Step 1: Initialize worker load and task counts}\\
Set worker load $U_w = 0$ for all $w \in \mathcal{W}$; taskCount$_j = 0$ for all $j\in \mathcal{J}^{\text{Low}}$\;
\\
\textbf{Step 2: Assign each job}\\
\ForEach{$j \in \mathcal{J}^{\text{Low}}$}{
    Assign worker $w^*$ with minimal $U_w$ if available on $R_j^{\text{Start}}$\;
    
    Schedule first task as direct work with $w^*$, update $C_{w^*s}$, $U_{w^*}$, set $cumProg_j = 1$\;
    
    $s \leftarrow R_j^{\text{Start}} + 1$\;
    
    \While{$cumProg_j < R_j^{\text{Dur}}$}{
        \If{$s > \max\mathcal{S}^{\text{Time}}$}{break}
        
        Compute $\alpha^{\text{Eff}}_j$ based on taskCount$_j$ and $\alpha^{\text{Eff}}_{type}$ and optimization parameters\;
        
        \If{full BW-window exists}{
            \If{QoS constraint not met and $C_{w^*s} > 0$}{
                Schedule direct work with $w^*$, update $C_{w^*s}$, $U_{w^*}$, $cumProg_j += 1$\;
            }
            \Else{
                Schedule automation, taskCount$_j += 1$, $cumProg_j += \alpha^{\text{Eff}}_j$\;
            }
        }
        \Else{
            \If{$C_{w^*s} > 0$ and $R_j^{\text{Dur}} - cumProg_j \geq 1$}{
                Schedule direct work with $w^*$, update $C_{w^*s}$, $U_{w^*}$, $cumProg_j += 1$\;
            }
            \Else{
                Schedule automation, taskCount$_j += 1$, $cumProg_j += \alpha^{\text{Eff}}_j$\;
            }
        }
        $s \leftarrow s + 1$\;
    }
    \textbf{Step 3: Ensure last task is direct work}\\
    \If{last scheduled task is not direct work}{
        \If{$C_{w^*s_{last}} > 0$}{
            Replace last automation with direct work, update $cumProg_j$\;
        }
        \Else{
            \While{no direct work assigned}{
                Compute $\alpha^{\text{Eff}}_j$ for next automation session\;
                
                Schedule automation, taskCount$_j += 1$, $cumProg_j += \alpha^{\text{Eff}}_j$\;
                
                \If{$C_{w^*s_{next}} > 0$}{
                    Schedule direct work with $w^*$, update $cumProg_j$, exit loop\;
                }
            }
        }
    }
    Calculate $COST_j$\;
}
\textbf{Step 4: Return solution}\\
Return $z_{jws}^{\text{High}}, u_{js}^{\text{High}}, COST_j^{\text{High}}$ for all $j \in \mathcal{J}^{\text{Low}}$\;
\end{algorithm}

\end{document}