Some options:

Hard tubes like these. There are other ones on Amazon for larger sizes.

You can fit multiple mats in a tube.

https://www.amazon.com/FVIEXE-Blueprint-Telescoping-Adjustable-Expandable/dp/B09GBD37CM/ref=mp_s_a_1_12?crid=1HIVXWZSFVMZ4&keywords=extendable+storage+photo+tube&qid=1670982334&sprefix=extendable+storage+photo+tub%2Caps%2C339&sr=8-12

Or a wall a paper storage bag like this. See through, which is convenient, cheaper maybe?, holds more in one tube.

https://www.amazon.com/ZOBER-Organizer-Standard-Wrapping-Waterproof/dp/B079HF9WQR/ref=mp_s_a_1_5?crid=QEXK1MPSWXKJ&keywords=cylindrical+storage+bag+tube&qid=1670982464&sprefix=cilindeival+storage+bag+tu%2Caps%2C384&sr=8-5

Photography tripod carry case. Multiple lengths, zipper on soft fabric, decent price.

https://www.amazon.com/Vidpro-TC-45-Tripod-Carrying-Case/dp/B07RQVVSX2/ref=mp_s_a_1_1_sspa?crid=APA8IS3WCTMB&keywords=photography+tripod+bag&qid=1670982584&sprefix=photography+tripod+ba%2Caps%2C397&sr=8-1-spons&psc=1&spLa=ZW5jcnlwdGVkUXVhbGlmaWVyPUExUjFRN1RFUjNLVFlRJmVuY3J5cHRlZElkPUEwNDU2NjEyM0w3UVlSVUJQNjY1QSZlbmNyeXB0ZWRBZElkPUEwNjgwNjk2MklBTkFGNVdURzlWQSZ3aWRnZXROYW1lPXNwX3Bob25lX3NlYXJjaF9hdGYmYWN0aW9uPWNsaWNrUmVkaXJlY3QmZG9Ob3RMb2dDbGljaz10cnVl