Picker pill is only painted in the expanded sidebar, but
workspace_picker_open lived independently of sidebar width. If a user
opened the picker, then collapsed the sidebar via the toggle or by
dragging the resize handle below the COLLAPSED threshold, the popover
state stayed `true` — re-expanding the sidebar would surprise them
with a stranded popover from before.
Drop the picker_open flag inside set_active_sidebar_width whenever the
new width is at or below COLLAPSED_SIDEBAR_WIDTH_PX, so the popover
state stays in sync with the trigger's visibility.