Assuming it is your website and you like to automate manufacturing after a client or employee has successfully inputed a form.
You usually create a mvc web app. Model View Controller. Your View is a typical web client app such composed out of Html/CSS/JS or frameworks like React, Angular, Vue, Blazor etc…
Then you have an controller and this is basically creating endpoints for your (rest) api.
It takes for instance your form data and processes it further to your model.
The Model can be a database or an wrapper to communicate with Rhino, Grasshopper.
Now writing such a wrapper is tricky, because it has to take use of interprocess communication. You want to schedule manufacturing, you have to be sure Rhino is running and ready to receive data etc.
So what kind of people do you need? I think the second part is much more demanding. So you need a good .net (desktop app) developer with little experience in asp.net to create your mvc model. If the clientapp requires an frontend/fullstack web developer depends if this form is publicly available and requires a lot of attention regarding performance, security and design. I would stick to .net technology because you use it in Rhino,Grasshopper as well (C#,VB.Net,Ironpython).