I always equate "depth" with "time".
The longer it simmers, the more depth it gains.
Adding anything you mentioned at the end may punch up the flavour, but I'd consider it to be 'top end' rather than 'depth'.
My first thought would be to drop it in a slow cooker & see how it is in 4-6 hours - with or without your added ingredients, ...
Not an uncommon problem apparently.
that last link is someone cooking it in a pan. But there is some logic going on in those discussions. Soap is - animal fat + other ingredients. Some of the discussion is suggesting that perhaps your water is contributing ...
Maybe it's not soap that you taste. At least here in the US, most chicken bound for the supermarket is sprayed or dipped in a bleach solution. It could be you are picking up on that, but it is not a taste I've ever noticed.
While both recipes will produce "cooked chicken thighs", the intended texture of the result is different. In the case of slow cooking, the temperature is meant to be high enough to render out fat and convert collagen into gelatin. The texture of the meat itself will be somewhat stringy and shreddable, with some dryness (hopefully compensated for by ...