I guess the point here is that everyone will have individual responses to their baby crying. A recent study showed British babies cried more than other babies around the world. I don't know tge reason researchers suggested for this, but I suspect high and unrealistic expectations of motherhood is a factor.
Personally, I would do everything I can to stop all crying/grumbling/shouting (whatever baby upset might be labelled as) as soon as it started. I certainly would have hoped to have found something to stop my child being upset by the time it gets to screaming.
I'm someone who responds quickly to any cry or upset, certainly in the first 12 months of baby's life when they are entirely dependant on you for every aspect of their physical and emotional needs.
At 9 months, baby is crying for a need. Sounds like the need is comfort in your baby and it would seem that your baby cannot access comfort in any other way that from you.
I am pretty sure that your baby would much rather be able to comfort herself, rather than screaming to such an extent. I'm sure if she could self- comfort, she would. Its nor personal, she just can't.
Letting her scream in the hope that the screaming will teach her something... that's probably not the most productive method for long term healthy sleep habits.
When she's a little older, more like 12m plus, she'll then have much improved fine motor skills. When she can use her pincer grip, pick things up turn them over and the right way around, place objects with accuracy rather than dropping them... these are all the kinds of skills she needs to be able to physically self comfort.
She might then learn to tickle her own skin, play with her hair, rub her lovely in a specific way she likes, suck her teddies ear.. or many of the other ways babies learn to self comfort.
For now, her motor skills will be rudimentary and simplistic. For now, she needs you because she has no other way to sooth herself without you.
By all means introduce things for the longer term. Dummy, comforter, patting movements you do while breastfeeding, to associate with comfort. A sidecar cot is a good idea so you are sleeping separately, but also together.
But realistically, you just need to accept your baby needs you to sleep because your baby hasn't (yet) been taught any independant settling techniques. So teach her. And in the mean-time comfort her so she can get as much sleep as possible.