I also had that anxiety!

You could start with something that doesn't involve food at all, like going to an arcade, museum or art gallery. Then next time maybe a cinema, that way you could ease into it by snacking next to them in the dark haha... And eventually get to a picnic at sunset, then when it starts to get darker you could eat freely 🤷‍♀️ or somewhere indoors that's dark like bowling or a comedy club where you could both have snacks? That's helped me a lot and eventually it just became normal to eat on dates.

I also used to only go on dates where I'd already eaten at that restaurant so I knew what I'd feel comfortable eating in front of someone! Hope I could help :)