It sounds like the best thing for you is a clover lawn, although of course it will only "look like grass" from a distance.
Recently, after noticing that many homes in my neighborhood have large patches of clover in their lawn, and knowing how difficult it has been to battle in my own lawn, I did a search on it.
Instead of finding many resources on how to get rid of it, I found it is actually considered/promoted by many as a lawn alternative, or combination for a healthier lawn.
This article from
The Spruce lists the following qualities of clover lawns:
It stays a luscious green all summer, without being irrigated profusely (i.e., it's drought-tolerant).
It is free of weeds, obviating the need to apply herbicides.
Your carpet competes so well for growing space that the competition is choked out.
It doesn't need to be fertilized.
It is also relatively pest-free, so that you don't have to bother spraying pesticides on it.
It aerates the soil on its own, so that you don't have to worry about counteracting soil compaction.
It is soft to walk on.
It attracts beneficial insects, including honeybees.
It rarely has to be mowed.
It doesn't suffer the discoloration from dog urine known as "dog spots."
And if, despite all these benefits, you should ever want to replace it with a different kind of green carpet, it helps you to do so by improving the soil on its watch.
Its ability to aerate the soil and pump nitrogen into it means that succeeding generations of plants using that soil will be better off.
Other resources on this topic: Cloverlawn — Benefits and how-to Earth Easy — Attributes, benefits, and prices of clover and other lawn alternatives
gardening.stackexchange.com/users/81/Nicole
I planted "shorty mix" from DirtWorks (company no longer in business): 40% Discovery Hard Fescue 30% Blazer IV Perennial Ryegrass
30% Moonshadow Kentucky Bluegrass
It does not grow very tall or very quickly and does not need frequent mowing.
I also knew some people who planted a low-growing clover on their lawn that they almost never mowed.
It got a little high in midsummer (maybe 8") but still looked decent, and was always green.
gardening.stackexchange.com/users/51/bstpierre
I know it sounds crazy, but part of my backyard is filled with wild strawberries.
They don't grow to be very tall.
I only have to mow it when the other weeds get tall.
It's kind of fun to walk on in the spring because of the red berries sprinkled in the salad!
I'm not sure where you would get enough seed for a lawn.
gardening.stackexchange.com/users/168/agent-j
If you've got a shady spot that grass has a tough time growing in, you might be able to let moss cover your lawn.
Through sheer neglect I have adopted this strategy with good results.
Walk on it with bare feet though, it feels good!
gardening.stackexchange.com/users/10/Peter Turner
You could plant garlic chives.
Market gardeners have fields of them.
They are a perennial flat leaved grass like plant that grow about a foot tall.
They don't usually have pest problems and attract butterflies.
Instead of mowing them, just cut enough to eat or make jiaozi.
You could also cut and sell.
They contain a healthy dose of folate.
Like all the alliums (garlic, scallions, onions, etc.), chives contain heart-healthy allicin.
Allicin has been shown to help with cholesterol issues and lower blood pressure.
They thrive in colder climates and struggle in intense heat.
gardening.stackexchange.com/users/1894/Graham Chiu
White Clover is a good choice and depending on water conditions may not require mowing.
Vinca minor or Lesser Periwinkle is a maintenance free choice which tolerates partial shade and is available with several flower colors and variegated varieties.
gardening.stackexchange.com/users/20571/herb guy
perennial peanut - very hardy low lying bright yellow flowers and a good nitrogen builder
gardening.stackexchange.com/users/26964/Dori Bon
I don't like mowing my lawn. Is there a grass replacement plant which:   looks like grass,  one can step on it,  does not need mowing?
What is a good grass replacement plant?
gardening.stackexchange.com
<lawn><plant-recommendations>
gardening.stackexchange.com/questions/201
gardening.stackexchange.com/users/75/asalamon74
You could try planting clover, such as white clover, or moss. Why not give over some of the space to wild strawberries? It sounds like the best thing for you is a clover lawn, but you could even plant wild strawberries.  If you've got a shady spot you might be able to let moss cover your lawn.  Or you could also plant garlic chives or perennial peanut, which  is low lying with bright yellow flowers and a good nitrogen builder
It sounds like the best thing for you is a clover lawn. You could even plant wild strawberries.   If you've got a shady spot you might be able to let moss cover your lawn.     You could also plant garlic chives. Perennial peanut is low lying with bright yellow flowers and a good nitrogen builder