I use a tablet, laptop, ipad, iphone, google nest hub and so on all at the same time.
one device uses the standard interface other ha a special interface i access.
Nest hub (home assistant cast)
tablet and ipad (HAdashboard)
iphone (homeassistant app)
while my raspberry is tucked away for safe keeping
but to come back to your original question:
I wanted to install home assistant on my raspberry pi, but wanting to connect a touchscreen monitor I wanted to understand if I could use home assistant directly from him, or if necessarily from a remote desktop.
it depends on how you install it on your raspberry pi, if you use raspbian with desktop and then run hassio in a docker you can run a browser on the desktop an open the hassio page. if you install the raspberry pi version of hassio i think you willl only see the prompt.