As far as I understand, in a CQRS-oriented API exposed through a RESTful HTTP API the commands and queries are expressed through the HTTP verbs, the commands being asynchronous
There is nothing stopping you from doing that. If you execute your commands synchronously and create your projections synchronously, then it will be easy for you to just make a query directly after executing the command and returning that result. If you do this asynchronously via the rest-api, then you have no query result to send back. If you do it asynchronously within your system, then you can wait for the projection to be created and then send the response to the client.
The important thing is that you separate your write and read models in classic CQRS style. That does not mean that you cannot do a read in the same request as you do the command. Sure, you can send a command to the server and then with SignalR (or something) wait for a notification that your projection have been created/updated. I do not see a problem with waiting for the projection to be created on the server side instead for on the client.
How you do this will affect you infrastructure and error handling. Also, you will hold the HTTP request open for a longer time if you return the result at once.