Is the Cocoonababy nest mattress SIDS approved and safe to use as an everyday mattress for newborns?

Red Nose does not approve any specific brand name product.
There are a number of concerns in relation to some portable sleep space products for infant sleeping position.

Red Nose recommends that the safest place to sleep baby is in a cot that meets the Australian Standards, on a firm, clean, well-fitting & flat mattress.
https://rednose.org.au/article/what-is-a-safe-mattress
https://rednose.org.au/article/what-is-a-safe-cot

Many products on the market today do not promote a firm & flat surface.
There is a risk to baby of being placed to sleep in a position that may facilitate baby’s neck being flexed to the “chin on chest” position.
There have been accidents associated with bouncers, rockers and hammocks such as falls and entrapment, but the biggest hazard is the risk of a fatal sleeping accident.
When a baby is put to sleep in one of these devices, their head can roll forward, blocking their airway.
https://rednose.org.au/article/baby-products-you-dont-need

When a baby falls asleep in a propped up device the head can fall forwards, pushing the chin down towards the chest.
This can lead to the airway becoming blocked and reducing airflow.
https://rednose.org.au/article/bouncinette

Also, portable sleep surfaces, like the one you describe, do not have Mandatory Australian Standards for safe infant sleep.
All safety standards for products in Australia are developed & monitored by ACCC - Product Safety Australia - https://www.productsafety.gov.au/products

Placing a baby for sleep on their back & flat (not elevated), is the safest way for baby.
Baby’s swallowing & arousal mechanisms work more effectively when flat & on the back.
Babies are at risk of “chin on chest” position when not lying flat, which may increase risk of compromising baby’s airway.
https://rednose.org.au/news/why-should-you-sleep-your-baby-on-their-back

Red Nose does not recommend restraining a baby in any one position while sleeping.
https://rednose.org.au/article/is-it-safe-to-use-products-designed-to-keep-baby-in-a-particular-position