Do I absolutely need a tripod and a mirrorless camera?

That is not what you need to demand: what matters is the plate in the light of your table. A tripod helps in low light, and it is in the way if it blocks the pass while the shift phone already covers the story. Leave space by the table so the kit does not cut the kitchen's path. In Madrid the camera brand gets debated and the plate on the menu stays dark. The folder you take is judged by the plate, not by the body that shot it.