If you want an expanse of mulch, the only options are hand weeding it or spraying it with Round up.
Almost no one hand weeds. So when you see an expanse of mulch, it’s probably maintained by a contractor using spray.
If you want to manage your yard without round up, you have to plant densely or weed a lot. Nature abhors a vacuum.
As for the ants, the ants are allowed to live. You’ve got to unclench. Or pave your whole property.
The best option for you is probably just to hire a yard crew. They will add mulch and spray it periodically and you can just not go out there, thus avoiding the ants.