Don't feel bad.
No matter what, a baby needs sufficient daily intake and especially during growth-spurts.
You said you have difficulty with supply.
Did you see a Lactation Consultant? If so, then try that route, too.
Does your baby latch on, properly?
If not, then seek a lactation Consultant to help, too.
Now: FULL or not, a baby wakes.
A full baby... does not, not wake. They wake too.
6 months is a time of: teething, growth-spurts, more hunger, and time of MANY developmental changes and hitting milestones. ALL of these things, occur at one time. Not one at a time. THESE things, tweaks a baby's sleep, too.
Now, yes, if baby is not getting enough intake, you need to supply her with adequate intake, per her appetite, and if that means giving a chaser of Formula, then fine.
Try, to give the Formula as a 'chaser' after nursing. NOT to replace, a nursing. Otherwise, your milk supply will drop, further.
Also, if on solids, ALWAYS nurse BEFORE solids, not after. If giving nursing after solids, baby will be too full to nurse, and this will cause weaning from breast. This is also per our Pediatrician.
I breastfed, both my kids They both had GINORMOUS appetites. 24/7.
With my son though, he started to hate breastfeeding and by 1 year old, weaned himself. Then he had bottles.
He had a HUGE appetite, I nursed using both breasts per session, he'd drink me dry... and STILL wanted more. THUS, I at times, had to give him Formula as a chaser. AFTER nursing, from both breasts. Though I had plenty of breastmilk. My Pediatrician was aware of this.
The MAIN thing is: that your baby get adequate intake, daily. 24/7.
If not, then a baby, will be constantly hungry and sure, not be able to sleep.
But other developmental occurrences, tweak their sleep, too.
Regardless of having a full tummy or not.
Also, feed baby on-demand. NOT per a 'schedule.' Otherwise, baby will not be getting adequate intake nor will it reflect her growth-spurt changes and needs for more intake at these junctures.