Before 4 months, dd was in a moby all the time. I could do a little cooking, but not a ton. We ate out a lot, and dp was a big help. As far as eating, I could still fit in a booth with her on, and I'd just eat over her. Carefully. Yes it was a bit messy, but not so awful. I'd put a napkin on her head when possible. Sometimes DP and I would take turns eating and doing laps with the baby.
At 4 months I discovered back carrying, and then cooking was easy. I cooked with DD on my back in a wrap or Mei Tai and later in a Beco.
At 5 months, I discovered that DD could sit in a high chair, so she sat and played with toys while I ate (sometimes). That was handy since she was getting grabby around then.
Even at 12 months I still occasionally end up eating with a baby in my lap, but it's much more rarely. Like maybe 1x/wk. And even then, sometimes DP is there and we can take turns (but now we don't have to do laps - she's content to be in a lap at the table). Of course, now she eats at the table which brings a new set of challenges!!
If I were to do it again, I'd do a back carry much sooner to help with the cooking. I'd consider a high back carry while eating too, if the babe doesn't mind. I don't think it would work in a booth, but I can usually turn the chair sideways and eat if, say, DD falls asleep on the way to a restaurant. And some chairs have low enough backs that a tiny baby would sit above the back anyhow so I think that would be pretty comfortable.
Learning a high back carry with a small baby is a little scary and tricky, but totally worth it. I found it easier to learn it with a Mei Tai.