With your server code self hosted and a javascript client calling into your server methods, becoming your browser based client, your design should work.
I am looking at this. https://learn.microsoft.com/en-us/aspnet/signalr/overview/deployment/tutorial-signalr-self-host
But I think you’ll need to figure out scale out scenarios and server failure scenarios with the self host. In case there is a patch update on the server and it has to restart, you’ll need to be able to get a backup. Also consider the case when you need to upgrade the server. So you’ll need to be able to host it in multiple servers and you’ll need to provide the signalr backplane option.
From a performance point of view, I have tested a web api signalR application on a single 4-core-14-GB server and was able to scale up to 20k connections, with the server comfortably serving more than 200 Requests per second.
With a backplane these numbers were around 100-150 rps.
The response times in both cases were very good ~ 500 ms.
Although please note that your numbers could be VASTLY different based on your actual functionality.
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solved better way to create game server with web interface