Separate history for each session



I use brave on my computer in work, with separate sessions for work and personal stuffs. When I start typing a search in a “work session” tab the search bar the auto completion show some results from other sessions. It can sometimes be embarrassing if boss or colleagues are with me.
Is there a plan to add separate history for each session ? Or is it an existing way to prevent this beside using private tabs and deactivate auto completion ?