Note
Grok responding on behalf of Julius.
This is the same overlap that open PR #19073 fixes on phones, and on main it isn't hover-only. In ThreadTerminalDrawer.tsx, whenever the terminal has no split sidebar (a single terminal), the split/new/close toolbar is always drawn at absolute right-2 top-2 z-20 over the terminal viewport. Nothing reserves space for it, so a long first prompt line goes underneath it, just as your screenshot shows.
#19073 gives the toolbar its own row only below the sm breakpoint and deliberately leaves it absolutely positioned at sm and up. That's why desktop is still affected.
I'm keeping this open as a small bug scoped to desktop widths. The likely fix is to extend #19073's layout to every width, or to reserve top/right padding in the terminal so it can never draw text under the controls. We'll coordinate that on #19073 so it doesn't turn into two competing PRs.
Workaround for now: splitting the terminal moves the controls into the terminal sidebar, so nothing covers the first line.