Sure, I'd love some feedback on my profile. Whatever you've got.

I put separated in my profile. What that means is that I am married and my wife is living in an adult family home in the last stages of dementia (she's only 62). I'll stay married for as long as she lives, which could be a day or it could be years. I am looking for friendship first but I am open to a relationship even while my wife is still alive. I will still love my wife and continue grieving for her at the same time.

What I've done is, if I connect with someone and we're chatting, I'll tell her about the situation in the first or second message, so they can make a choice early on whether or not they feel comfortable with it.

(I am getting silence from someone I forgot to tell for longer than that and was just told. I have a feeling she's not happy about it. I don't know how it slipped my mind, but it did.🤷‍♂️ )

There's no point in telling that story here. This is a forum. You got to put a bit of explanation of the situation in your profile text. And if hoping to eventually get a new relationship you will have to make very clear that your wife is no hindrance given her condition.
If it feels odd or wrong to you to put that in your profile that way you simply shouldn't be on a dating site.
You've got to be ready to really give a new woman a fair chance at love with you so no one who's full of hope & ready for love falls victim to your situation.

^^^^ Basically what Crystal said! There is no way of sugar coating this for you. You need to put married in your profile and not be dishonest to anyone. Any way you slice it it will be better to be upfront, but the truth remains you are married and want action on the side. Regardless of her condition doesn't she deserve better than you being unfaithful?