Selling first removes financing risk. You know your net proceeds before you commit to a new purchase, and you avoid carrying two mortgages or a bridge loan, at the cost of needing a flexible possession date or temporary housing if the timing does not line up perfectly.
Buying first gives certainty on the new home but adds cost and risk here: carrying two properties, a bridge loan's interest, and the pressure to accept a lower offer on University Heights because you need the sale to close by a fixed date.
The right order depends on your equity, your risk tolerance for carrying two properties, and how firm your new closing date really is. Get your hand-reviewed valuation from Joel Dyck.