There are ways to remediate your backyard enough to make it safe, but only if you really want chickens. You can do most (all?) of the labor yourself but the cost of materials will probably dwarf any savings from the eggs - especially since you probably already have better quality eggs available locally than what we Americans are used to, which I think is the real impetus for most people rearing chickens here.

The first step is to dig up a decimeter or two of soil (the more the better) from the area you want to build your chicken run and dispose of it safely which your city government should be able to advise you on. Next you deposit a layer of clay, 4-5 centimeters thick, wet it and compact it so that any weeds or grass growing in the area can’t grow roots down into the contaminated soil, then cover it up with uncontaminated dirt that you truck in (that last bit is usually the expensive part). You can also use cement instead of the clay and you probably want raised borders so the roots can’t grow laterally either.

My city provides mulch for free so I used that as most of the fill, compacted it, then just put cheap dirt over it. The big cost is testing afterwards to make sure it really is PFAS free but my family is paranoid and it’s a small price to pay for peace of mind.