Plumbing – My gas water heater’s T&P relief valve is leaking. Can I safely close the heater’s supply valve & leave the gas on

I'm not a professional plumber (though I did work on water treatment systems for several years), but in my opinion what you did is fine.

Gate and globe (stop) valves are prone to corrosion and generally wear out over time. Ball valves are much more durable and reliable. I've seen many, many old stop valves that are leaking or don't shut off properly, or more often, leak as soon as you open/close them after they've not been touched for years. I can't say the same for ball valves - I've seen many that were installed for many years and still worked. I can even think of a couple where the outside looked totally corroded, and though it took a lot of force to turn (and sometimes a replacement handle), they still reliably shut without leaking.

On top of the reliability, the fact they use a 1/4 turn (instead of several full turns) and a quick glance tells you whether it's open or closed, ball valves are just vastly superior to gate and globe valves for almost all residential applications. Worth the extra dollar or so they cost.

The only thing they are not as good for is applications where you want to limit/control the flow rate (such as an outside tap or sample port). They can still do that, but are harder to finely adjust, and especially when one hasn't been opened for a long time and is a bit stiff, tend to suddenly give and open to full blast (I've been sprayed while trying to take water samples many times).

Any valve that refuses to fully shut off won't be improved by tightening the handle further.

The usual problem with a Globe Valve is that the rubber valve seal has aged and cracked, needing replacement. This means you have to shut the water off upstream of the valve and remove the body cartridge so the rubber seal can be changed out.

Some valves have a globe shape, but get misidentified by that shape because they actually are Gate Valves which have a vertical wedge shaped metal gate that gets pushed down into a tapered slot. These fail because sediment accumulates in the slot on the downwards side and the gate no longer can be pushed fully home so the taper seals. This requires the water to be turned off upstream so you can take the top off the valve, extract the gate and grub the sediment out using a piece of welding rod so it will flush out when you reassemble the valve.

I've gone over to using quarter turn ball valves when I have to go to this much trouble. They are better than Globe Valves because the opening is the same size as the inner diameter of the pipe when the valve is full open, the water doesn't have to turn 90 degrees to flow through a restriction as it does in a Globe valve and while the gate valve has the same lack of restriction as the ball, the ball valve has no slot for rust, sand and sediment to accumulate in while it spends most its life wide open.