See last paragraph, and sibling comment: not really needed (except for extreme cases like preserving the last of a species). Plus I have a job and hobbies already :) Moreover, it's still not a very sustainable solution: you can get all the locally grown seeds you want, if you sow them in unfit soil (pH/moist/minerals/...) and/or soil which is just too rich in nutritients it's still no use and they either won't grow at all or get overgrown by grasses/nettles/... Especially the nutritiens are a common problem can usually also be solved by proper management (which more often than not starts off simply by mowing 2-3 times a year and removing the cuttings).

Or maybe just stop cutting your lawn so often. With proper management it will get colonized by local species in a few years.

Genuine question: what is proper management?

Genuine answer: it depends. I guess you just have to be present and observe what is going on and try to get closer to what you try to achieve.

What works all the time is to not cut the whole place at once: so insects have another places to move to. I am also trying to make sure grasses don't take over the place.

But the thing is: even on my few acres spread in diameter of few kilometers I am getting very different results.

Few kilometres, amount of shade, amount of water in the soil, different type of soil, different history (e.g. used to be farmland or used to be forest) can all be reasons for different results. But yes definitely don't cut everything at once, that ruins the habitat. For the rest main problem is usually nitrogen deposition so key is cutting and removing cuttings to compensate for that i.e. remove nitrogen again. And the time at which mowing gets done is pretty crucial as well and requires some experience with the specific terrain as you point out. But there's way to much nuances to all explain here. By far the easiest way to gain knwoledge imo is finding a local nature organization which manages grasslands in your neighbourhood and see what they do/talk to them. I did that a couple of years and it's amazing what I learned from them (though in all honesty the people there are true specialists when it comes grassland and it's fauna specialists, it's also their daytime job, and there's like nothing they do not know - not everybody is that lucky)

A moving target! :)

Not suggesting this is for your lawn, but you might find this [0] to be an interesting read.

It's subject is people whose job descriptions are to answer your question, and how they are currently grappling with the subject of human-stewarded ecology.

https://www.newyorker.com/magazine/2020/02/17/can-farming-ma...

Two big things that help are don't fertilize it and don't water.