Well .net core api comes with built in kestrel server,which is light wight and cross platform. Although there are some limitation like it does not support port sharing and window authentication etc.

Microsoft suggest to use iis in front of kestrel for public facing websites.

if you have advanced requirement you can use full fledge server like iis, Apache or nginx.

This webapi project is not a giant or big project.
Its a small project.