It's mostly a deployment issue, if you want your api to coexist. Depends on also if it's serving any of the other applications in effect. so say your 2. 3. or 4. would also need to use it, that could advocate as to why to co-locate it, but often people choose to seperate the concerns, i personally have been going both ways, depending on aforemetioned, often we're serving http to devices etc and it makes sense not to have to deploy and debug seperate instances.
Anyway, most of us using .net use web api 2, unless .net core is an option. That's as easy as adding it from nuget and it works on webforms and mvc alike
NuGet Gallery | Microsoft.AspNet.WebApi 5.2.3[
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