Water – Can someone please explain this gas water heater thermostat marking

Obviously, there is some threshold or setting that needs to be adjusted, as when you go back to full hot it kicks back on. You need to adjust it so that full hot is not required to keep it on. All this you already know. Not being familiar with your particular unit, I don't know exactly what adjustments are available.

As I understand it, when you are on full hot, the water flow through the unit is greater, and the water does not get as hot (maybe, because the flow is greater), but you get more of it. The incoming water supply is cold, and it supplies both the heater and the cold water line, so when you start using both, the flow through the heater decreases. This would be the case even if you still had the shower set for all hot, but the cold water was turned on at the sink (try this - does the heater turn off, as it has before, mid shower?).

Then when you start mixing the hot and cold in the shower to get a pleasant temperature the flow through the heater is reduced again, because you are requiring less hot water. This may result in the heater turning off because the flow is less, or maybe it is turning off because the water is getting too hot. So either there is a low-flow sensor that needs to be adjusted to a much lower setting, or maybe there is an overheating cut off switch that is faulty or needs to be set higher.

You might try your shower again, as normal, but with the hot water on at the sink. Does this make your hot water stay on, as you want it? (Of course this is not a solution, but it might help you find the source of the problem). Hope this helps.

Only "power-vent" type gas water heaters can be vented with plastic pipe. These are gas water heaters with a fan on top which blows the flue gas (and cools it by mixing surrounding cool air with it, hence plastic vent is OK) out of the house. Most can be vented with 3" PVC (white), ABS (black), or CPVC (kinda tan colored). These vents can be run horizontally and can have 90 degree bends (limits on that though, see instructions/local code). So if the black pipe in question is plastic, it is probably ABS, and the vendor might be wrong.

Not sure if you know what you are getting into, direct-vent heaters are significantly more $$ than regular natural draft gas heaters (which require metal vent pipes that go more or less UP only). Some of these direct-vent heaters now require a fresh air supply from outside because they have sealed burners, you may not be equipped for that. You would need to be 100% sure of the condition, length, and route of the existing vent if you use it. Then there is the piping for water and gas and such, labor...

It might not be worth the trouble and expense to change back. Amortize the cost of the new heater over time and I am not sure it would pay off.