Apple supports this already on the ipad by making the ipad another screen for your mac (I think it’s called sidecar?) and still use pencil, mouse, keyboard etc.
Iphone is novel though, but does a pencil work?
My guess is this is meant to be a no friction VNC (though it doesn't seem to be using VNC). So you can be away from home and remote in.
There are VNC clients on iphone / ipad - but generally it's whole desktop.
RealVNC is the name brand but it's not exactly a good experience. "Screens 5" looks like a better alternative.
individual windows and touch are not supported by sidecar, afaik
Sidecar streams the mac display to the ipad, but it has to be initiated and controlled from the mac.
In contrast, what I wanted (what this app does!) is to view and control my mac from my handheld device, initiated from the handheld device.
These apps all look similar and it makes it very difficult to search:
• Mac screen --> Handheld, as extended display = Sidecar
Use-case: I use my ipad as additional window space for the mac.
• Mac screen --> Handheld, as duplicate display = Sill, Sunshine+Moonlight
Use-case: I leave my desktop and continue watching what I had playing on it from my kitchen ipad.
• Handheld screen --> Mac = Airplay
Use-case: I play some media from my iphone on the mac screen.
• iPhone screen --> Mac, controlled from Mac = iPhone Mirroring
Use-case: I use my iphone-only apps from my mac, wirelessly
• iPad controls --> Mac, controlled from Mac = Universal Controls
Use-case: I use my ipad with my mac mouse+keyboard
Usually, trying to search for this type of app obnoxiously returns results for Airplay, and if you manage to filter it out, it's Sidecar — but it's not what I want!