ladylotty - I hope it is getting better now? My DD1 was a terribly sleepy feeder and was asleep for most of her first week and I swear didn't open her eyes until the second. It was a shock to deal with as my DC1, DS, had been alert and crying for feeds regularly from birth. I managed to get her to feed more efficiently over time by stripping her for all of the feeds and if, she fell asleep, by putting her on the floor (had to be a cold, hard and draughty floor, as the bed or even a soft carpet was enough for her to get comfy and fall asleep again). After the first couple of weeks I felt the cycle had been broken and she was giving me the cues more than me watching the time and waking her for regular feeding. But it was hard work and so I wanted to say to you, "hang in there", as it can suddenly change for the better even though you will like it won't ever. I recall each of the toe-curling feeds during that time as I was so tired I was not ensuring a good latch and had cracked bleeding nipples from the start.
I also had to feed from one side as she had difficulty feeding from the other for the first 6 weeks (it has a larger nipple) and so also expressed every feed from the side she didn't feed from to keep the supply up and her intake up too. This meant that I was constantly sterilising and expressing but it did mean I could have a break from the toe-curling feeding every so often which, despite the extra work, was welcome at the time. So I do understand where you are coming from!
I have recently had DC4 and she also started life as a sleepy feeder. On the advice of an anxious midwife I took her to A&E at 4 days as she had lost 11% of her birth weight. I felt at the time this was probably her being over-cautious as all other signs were good (she was alert, wet nappies although slight meconium in poos still, not the yellow stuff) but of course on day 4 I was right in the middle of the Baby Blues and so was inclined to do what anybody told me at that stage even though I knew in miy heart that I just needed to be left at home to get her feeding more often and BFing established while my DH was on paternity leave and could focus on the other DCs. It turned out to be a huge PITA as the medical reaction was to be extremely cautious and admit her for monitoring of feeds where I had to express and feed her by bottle so they could record the quantities she was taking. Needless to say, after being discharged I had a further battle on my hands to get BFing properly established again! (cue: much cursing of the aforementioned midwife during this time!)
Anyway, I digress, because it sounds as if your problem is just a sleepy feeder and not weight gain as you have not mentioned other signs of problems. But my point is that I have had two sleepy feeders (I am not even going to mention DD2 who refused point blank to BF so prompting me to express to feed her BM) and various issues in connection with each of them, but after persevering, I managed to BF DD1 for a year and plan to do the same with DD3 for at least that long. Along the way I have had to express and bottle feed EBM, use nipple shields to get DD3 to accept the nipple again after feeding her EBM in bottles for 24 hours because of the sodding medical intervention and deal with one-sided feeding until the little burgers can get their chops around my larger nipple, but it has all been worth it and although it seems like an eternity at the time, it has really been just a minor blip in the grand scheme of things looking back now.
Just a thought: if you feel a bottle of EBM would help you, why not? Just be prepared for what that may entail for the relief it may give you (eg a bit of nipple confusion possibly and lots of extra washing and sterilising) and keep an eye on where it may lead you. I have used bottles very early on with mine for reasons described and found that I had to watch the ratio of bottles to boob to ensure it wasn't detrimental to the BFing. Now with DD3 I keep it to just one a day to keep her used to a bottle and find that more than twice can make it tricky for example. It is always a personal choice but watch you won't end up going where you would rather not!
PS - I have found the advice here and, in particular, that from tiktok absolutely brilliant from whom I have learnt much from (even on my fourth DC!) But do make sure you do what you want to do based on what you have been advised. You are the mum after all! Then if you mess things up you have only yourself to blame . But conversely, you can pat yourself on the back for the successes!