My black tea goes cloudy as it cools in the glass pot, hard water or bad leaf?

That is tea cream and it is a sign of a strong brew, not a fault. As the liquor cools, compounds that were happily dissolved at 95 degrees come out of solution and haze it. Strong black teas do it most and mineral heavy water makes it more obvious. It is the same effect that makes chilled black tea look dull.

Mild disagreement with treating this as purely cosmetic. The haze is harmless, but getting it strongly at five minutes off a full boil says you are extracting hard, and with Assam that also means pulling a lot of astringency. Try four minutes with slightly less leaf and see whether the cup gets rounder. If it does, the haze was a symptom of something worth adjusting, even though the haze itself was never the problem.

Drink it hotter. The glass pot means you are watching it cool for ten minutes, which is the only reason you noticed. Ceramic pot, a cosy, a smaller cup, and the problem disappears without changing anything about the tea.

I tested the water question properly because I was convinced my tap was ruining everything. Same leaf, same weight, same temperature, three waters: tap at whatever hardness my area runs, a bottled low mineral one, and distilled.

The tap brew hazed within about eight minutes of cooling. The low mineral one hazed later and less. The distilled one stayed clearest and also tasted flat and dead, which is the trap people fall into. Tea needs some mineral content to taste like anything at all. My conclusion was that a middling low mineral bottled water is worth it for something special and pointless for a mug on a Tuesday, and I stopped worrying about haze entirely.

I learned this the annoying way making iced tea for a party. Brewed a big pot hot, put it in the fridge, served eight people something that looked like dishwater. It tasted fine and nobody drank it because it looked wrong. Now if I want it clear and cold I either cold brew overnight in the fridge, which never hazes, or I brew double strength hot and pour it straight over a full jug of ice so the temperature crashes in seconds. It is the slow cool that does it.

One thing that is not tea cream and is worth ruling out: if there is fine sediment settling rather than a uniform haze, that is broken leaf dust getting past your strainer, and a finer mesh or a quick rinse of the leaf fixes it. Haze is uniform and vanishes if you reheat the cup. Sediment sinks and stays.