This has nothing to with HTMX/Hypermedia, this is an issue with SSR. No pure SSR frameworks can do this.
You would do this the same way you would in any other website, have the server send the data required (Hypermedia or not) and use client side JavaScript to do the client side reactivity.
This is like asking why doesn't HTMX allow me to change the colour of a button when I hover over it, why should I have to do this on the client?
Then use a different tool which provides the precise capabilities you are needing? I'm confused by your hostility. HTMX doesn't have to solve every problem to be considered viable.
You would do this the same way you would in any other website, have the server send the data required (Hypermedia or not) and use client side JavaScript to do the client side reactivity.
This is like asking why doesn't HTMX allow me to change the colour of a button when I hover over it, why should I have to do this on the client?