OP, I could've written your posts with both of my children.
They seemed to be breastfeeding all the time, no obvious latch problems, lots of wet and dirty nappies... yet lost weight and carried on losing.
With DS, we never figured out why he wasn't feeding properly.
After being sent back to hospital twice - and eventually accepting that breastfeeding wasn't working for us - I started exclusively expressing, with formula top ups at first until my supply caught up. He regained birthweight at 28 days.
Then, at 10 weeks, he suddenly started breastfeeding of his own accord. I'd been trying to latch him several times a day, and then he just did it.
We carried on bfing for a year. He's now three, on the big side for his age, and you'd never know how much trouble we had with feeding at the start.
Same thing then happened with DD, three years later.
Latch looked fine, feeding seemed to be going fine, but her weight fell and fell like her brother. Tongue tie diagnosed and snipped, but made things worse if anything.
She's now ff as - despite trying to pump every 3hrs round the clock - I didn't have the supply to pump for her. Goodness knows why, as last time my supply built up quickly, but this time it just wouldn't.
She's exclusively ff, well above birthweight now (at four weeks old), and is an absolute delight.
The most important thing, IMO, is to feed your child, however that has to happen. Formula top ups now will not necessarily jeopardise breastfeeding. Indeed, I'm convinced the formula made DS strong and alert enough to eventually learn how to feed from me.
Expressing is a pain. I've done so much bloody expressing I could write a book on it. When I was doing it exclusively, I had pumps for home, pumps for work and even a handbag pump. It's the worst of both worlds - all the faff of ff with the huge, leaky, engorged boobs of bf. I fully understand if you don't want to do it. It's a full time job when combined with trying to bf successfully as well. But it's probably time to accept that bf itself isn't working for your DD. You need another way, whether that's temporary formula or temporary expressing til the feeding problems resolve.
Right now it feels shit, I know. I've been there, twice. But honestly, having a well-fed and healthy baby is the most important thing and if you need a bit of formula, temporarily, to help you get to where you want to be (while investigating tongue tie, working on latch, breast compressions, maybe trying expressing etc) then that is no bad thing.
And if your DD ends up ff? She'll be fine. I wept when this happened to my DD. A lot. I felt I'd let her down. But she's thriving and I have to see that as the most important thing.