I am still getting the message "you have a pending trade offer" in Fake Pigskin.
I even get the yellow highlighted "Trade" menu link.

However, I do NOT have a pending trade offer.
There was an offer during the draft, which I accepted. It was draft picks for draft picks. However, when I accepted the offer, I received a popup message saying the trade could not be processed because it would put the other team over the cap.

We are now in Late FA Week 3, and I am still seeing the pending trade message every time I enter this league.

Are you in the preview site or the old site? I think the preview site will allow you to accept a trade that puts the other team over the cap as long as the next sim is not a game sim or training camp sim, but the old site will not. In any case, you are probably seeing the notice because the trade is still "pending" until it is cleared by a withdrawal or reject (or accept of course, if you are able to do that) - if it's preventing you from completing the trade it doesn't by default reject it.

It was on the old version.

The trade is for draft picks only, and the draft has already completed, so there is no way this trade can be accepted (or declined) at this point.

I've already cleared the message today. I'll let you know if I see it again tomorrow.