confuzed You are categorically NOT a failure. Look at that lovely baby you have there - YOU did that. You conceived him, you carried him and you gave birth to him. You keep him warm, safe and fed (however that may be).
BF is such an emotional thing, it's bound to be - it's a hormonally triggered process, but please, please don't beat yourself up about stopping. You've done fantastically :)
It's pure luck I've got this far with DS - with DD she was having formula top ups from 3 days old when the MWs put the fear of God into me by saying she was borderline for losing too much weight, and I stopped BF completely after a short time because I was too shy to do it in public and it broke my bloody heart, I felt a failure because I was putting her on 'the dreaded bottle' because I was embarrassed, not because of any medical reason so I understand. Anyway, she was of course fine, as are your lovely children, and there was nothing bad or wrong or shameful about using formula :)
Just as a thought though, if you're using bog standard formula then there's going to be lactose in that as well. It could just be pure coincidence that he's slept better and been chirpier during his awake time today, and nothing to do with the formula. If you want to try and keep up the BF then have you tried speaking to a BF counsellor or a lactation specialist or something?
DD largely ignores DS to be honest, she's been a bit funny with me and DH but is starting to settle a bit now. Bedtimes have been horrendous, and she won't let us out of her sight if she can help it - almost as if she's worried that we're going to suddenly produce another baby from somewhere if she takes her eyes off us for too long.