Currently we snap the tab title/alert indicator over to leave room for the close button whenever it's at all visible.  This looks super janky.

I tried animating the bounds over.  This only helps marginally, and only if the close button animation is the right speed.

I think we need to crossfade instead.  To do this, Tab::PaintChildren() has to actually paint all the children manually so it can implement the crossfading, and we need duplicate tab title/alert indicator members used only for crossfading.  The "real" members (children used in hittesting) should continue to be laid out as today; the paint-only members should be laid out based on there being no close button.  Then PaintChildren() can just alpha-blend between the two sets.