Are rugs like the mellow mat unsafe for a baby to fall asleep on? Are they too soft?

Play mats are not manufactured with safety standards/guidelines for sleep.
The general recommendation would be to move baby to normal safe sleep space when sleeping.
eg when doing tummy time and awake & supervised.

Never leave me alone or unsupervised on my tummy, as it is dangerous if I fall asleep or get my airways covered

https://rednose.org.au/downloads/RN0407_22_TummyTime_B_A4_0423.pdf