@Abitlost2
You definitley should not co-sleep if formula feeding. Formula fed babies are already at a higher risk of sids even without co-sleeping. Breastfed babies sleep a lot lighter in general and are more alert. Formula fed babies loose a reflect called natural arousal as they generally sleep much more deeply than bf babies.
Theres really no clear evidence that formula fed babies sleep more deeply/ are more difficult to reuse. There are studies that seem to suggest it and studies that suggest theres no link. And its always funny how when it comes to co-sleeping this is always asserted, but any other time its suggested that formula makes babies sleep more deeply/ wake less the suggestion is totally shot down by breastfeeding advocates.
Like I said before, I had pnd triggered by inability to breastfeed. I got very fixated on the increased sids risk and honestly I went to quite a dark place with it all, I really don't want to cosleep because of it but it really was the only way for us - it was cosleep or let baby scream for hours and I wasnt prepared for the latter.
Despite not being a magical unicorn breastfeeding mum, I found i slept incredibly lightly anyway and invariably woke up seconds before DD did, 14 months later I still do.
Ultimately there really is a need for more research/evidence about formula feeding and co-sleeping, though I'm not sure it will ever be done because of ethics. A big part of why its safer when you're breastfeeding is because of the position you adopt, and that's something I found I did naturally anyway (though probably because I'd read the lullaby trust info prior).
It's also worth saying again that the lullaby trust doesn't say you have to breastfeed to cosleep.
I'm not encouraging anyone else who is formula feeding to breastfeed, it really is a personal choice and it needs to be an informed one. But I do think the risk of giving a blanket 'no you can't do it if you're not breastfeeding, just no' makes it so much more likely that formula feeding mums won't bother reading how to do it safely and then end up, through exhaustion or desperation, doing it unsafely.