It sounds like you don't need a dishwasher.
I live alone. I don't use a dishwasher, I wash everything by hand.
It isn't hard. For example, I wash my plate when cooking food, which provides plenty of waiting time for allowing washing it. I don't have any other better uses for that waiting time, so the time usage from my point of view is zero.
Of the large items like pots and frying pans, they usually aren't intended to be washed in the dishwasher and if you do so, you need quite many of these so that you have enough of them for every day. So most people wash them by hand anyway.
Some items like drinking glasses and coffee mugs can be washed as needed, no need to wash every single day. If you drink only water, the drinking glass washing interval can actually be quite long, but coffee mugs require washing more often or else it affects the taste of coffee.
It's true that modern dishwashers are quite water-efficient so washing by hand definitely won't save water or the energy used to heat that water. So for the environment, it may actually be best if you just use the dishwasher and fill it only partially. The reason I don't have a dishwasher is not because it would be harmful to the environment to run it at quarter full. The reason is that it takes quite a lot of space for which I have far better uses. There's simply no reason to waste space for something big that I fill only partially. I use the space that the dishwasher would otherwise use for storing items (kitchen tools, food, etc).
If you really want to fully use your dishwasher, maybe you should consider putting your frying pans, pots etc. there -- buy many of these so you have a free one for every day. They take quite a lot of space so I can't imagine if you cook food that you would be unable to fill your dishwasher.
About a specific cleaning mode for half-full or quarter-full dishwasher: I believe they don't have that, since it's hard to automatically detect how full the dishwasher is. Washing machines can do that, since they have a rotating drum and they can measure the rate of acceleration of the drum with a constant power level to determine how much spinning mass the drum has.