My baby girl is 3 months old she is currently still in her bassinet at night but she has been moving over to the side and pressing herself against the mesh (including her face) I have made sure that the bassinet is safe sleep and she has her arms out in the sleep sack. I’m wondering if she needs to be moved into her cot yet? She can roll tummy to back but not back to tummy

Red Nose recommendations are to “always place baby on back for sleep” not baby must always sleep on their back.
https://rednose.org.au/article/red-nose-safe-sleeping-recommendations

Most babies will be getting close to rolling by about 3 months. Eg wriggling/moving around the bassinet.
Most babies will be rolling over by 4- 5 months. Some earlier, some later.
This is very normal as babies grow & become stronger.
Many babies then prefer to sleep on their side or tummy.
This is not something that needs to be stopped. It is important to make the “new” environment as safe as possible.
https://rednose.org.au/article/what-do-we-do-now-that-a-baby-has-started-to-roll-over  (please read full article)

Good to see you have stopped swaddling/wrapping but it is recommended to now move her to her cot.
Babies need arms free & the space of a cot to roll well & safely.
Ensure mattress is firm & flat & nothing soft or loose in her cot.
Continue to always place your baby on back for sleep.

How does she go with tummy time when awake?
Increasing tummy time when awake is important to build upper body strength to roll well (both ways)