This is how I ended up handling SessionID (like a real server would).
There is no need to handle session ids manually, since the common way of setting the session cookie is used. A browser receives it, stores it for the website and will send it automatically next time. (Like any website would.)
“Make it have a SessionID” gets the session id from the cookie. And stores it in sessionId
Simple memory gets it from $json.sessionId
Response sets the correct session header to return it
The Respond node creates a Browser-Session restricted sessionId. (will be removed when reloading the page).
To make it stay, change the respond node Value to:
SESSID_VueEngine={{ encodeURIComponent($('Make it have a SessionID').item.json.sessionId) ?? '' }}; expires={{ (new Date(Date.now() + 1*24*60*60*1000)).toUTCString() }}; path=/;