as you are looking for a client widget. asp.net core is immaterial as its the server side.
you can bundle your react as a widget (just create a build script), but you need a predefined html element to bind to, or additional javascript to bind. you will run into the same issue with any widget technology. office 365 and Sharepoint both support react widgets (they use a different build script rather than the react SPA template).
blazor WASM will have similar build issues as the default react SPA template (dependance on index.html), but while with react you can easily change the build, it not easy with blazor. also as the browser only supports one web assembly per page, you might run into conflicts.