Wobbly stem: serious issue or not?
That's an adjustable height stem. Looks like it has some sort of quick release and adjustment.

If it is irreparably loose it's a safety issue. The joint could collapse and the handlebar would drop down and forward suddenly.

Either: pass on this bike, or negotiate a lower price with the seller and plan to replace the stem. You'll need a riser stem for a threaded steerer tube. These are not too costly and easy to install with common tools, usually just a couple of sizes of hex wrench.

BTW, the brake lever angle looks wrong, seems to be angled down too far. Levers should be in line with your arms when sitting on the bike.