Can’t sleep train till BF baby can separate nursing from sleep- help!

As the title suggests, my 4.5 month old is nursed to sleep 90% of the time for bedtime and naps. We’re in the midst of the 4 month sleep regression, waking 2-3 times per night when up until a week ago she was sleeping 8-9 hours straight. The main barrier to sleep training is that she absolutely will not nurse in any meaningful capacity unless she’s drowsy. Fully awake feeds are distracted snacks at best, and I don’t know how to fix that either so that I can start to separate feeding from sleeping. Typical schedule:

• wake up 7/715
• bedtime 8 pm (bedtime routine starts at 730, bath, PJs, books, diaper change then nursing starting at 8 that often takes me 30-60 min to actually get her down)
• 3-4 naps averaging 25-40 min in duration. Rarely she’ll connect 2 sleep cycles and do a 1.5 hour nap.
• WW (usually) 2/2.25/2.5/2.5
• dream feed around 10pm before I go to bed The last week she’s been waking at 130am and 5am and won’t go back to sleep unless I nurse her to sleep.

She gets 2 bottles per day from dad while I work and similarly has a hard time finishing a bottle when wide awake so it’s not unique to breastfeeding. I know I have to separate feeding from sleep by 30 min, I’m just at a loss of how to do this if she’s too distracted to actually eat if she’s wide awake. I always nurse her alone in a dark room with no one else allowed in the room but she still fusses and unlatches and just won’t take a full feed unless she’s drowsy before sleeping 😭 this nursing conundrum has been going on for the past month and I’m so annoyed this is how it’s worked out. I’m worried if this cycle continues she’s going to become reliant on nighttime calories and not get enough day time calories and thus wake out of true hunger. My first was sleep trained and sleeps beautifully but she wasn’t breastfed so this is new territory for me. I don’t know if this is the right forum for my problem but figured I’d ask!