My 4 month old rotates fully in his bassinet. Arches his back and kicks off the side eventually turning him a full 180. Does this mean I should transition him to his cot or will staying in his bassinet be ok? I don’t want to transition to cot yet as it’s recommended to sleep in same room until 6 months

Some babies do wriggle & squirm & move around in a bassinet.
He really needs the space of the cot now.

Most babies are rolling by 4-5 mths - some earlier, some later.
The recommendations remain the same regardless of age.
Still always place baby on back for sleep.
Cease swaddling/wrapping
Move to cot from bassinet.
Baby needs arms free & space of a cot to roll safely.
https://rednose.org.au/article/what-do-we-do-now-that-a-baby-has-started-to-roll-over

Room sharing is recommended for the first 6 mths, but a safe environment takes priority over room sharing if there is not the space for a cot.
Check baby during the night - eg when you wake up/get up during the night.
“Parents are not expected to observe their baby constantly. If your baby is sleeping in a separate room check baby regularly to ensure that the baby remains on the back and the head and face remain uncovered”
https://rednose.org.au/article/room-sharing-with-baby

Also, keep the tummy time up when awake.