What version of software are you working on? (there's been some great improvements with the Server Technologies and the detection thereof in the last few versions) - you can find the current list for v16.0 here: https://techdocs.f5.com/en-us/bigip-16-0-0/big-ip-declarative-policy-user-guide/declarative-policy-additional-information/declarative-policy-appendix-available-servertech.html
My gut feel is that the .NET core signatures are included in the ASP.net packages, as they don't have their own entries, but I'm no expert on those languages. I would probably go with those to start with and keep an eye on your learning suggestions; if ASM has a better suited Server Technology, it will give you a recommendation at some point. (in the few latest versions at least)
Hope this helps.
I checked with v13 and v15, both only have ASP.NET and ASP only. I didn't see .net core.
I started with ASP.NET and I hope this will be enough for the ASM
I didn't see suggestion to add new server technologies