I can't really understand what you're describing. You have form on left & results on right, but you're requesting the new form state & re-rendering the form HTML on each request? Why? My naive understanding is that you could use something like hx-target to have the response to the form submissions update only the results area & the form should not need rerendered at all.
Why does the form need rerendered on a per request basis? HTML/Browser already tracks the current form state.
Why does the form need rerendered on a per request basis? HTML/Browser already tracks the current form state.