How publish balzor server with api in the same solution?

It doesn't matter how many projects are there in a solution, you can always deploy any project to any server.

Just right-click on your API project and publish it to a folder and then add that folder to IIS www-root as a website.

Do the same for Blazor project.

It is better to first publish the API project to IIS, publishing API is similar to publishing any web project.

Then on your blazor app use the URL of hosted API (just modify the localhost URL with the newly hosted API URL inside appsettings.json)

and then publish the blazor app.