Make a short mat (similar to the one shown above) that you can hang on the side. Use a strip of sticky velcro along the side edge of table.
Another option is to make one that can sit beside the machine area. You can use a clear photo stand to hold the organizer.
https://sew4home.com/projects/fabric...room-or-office
Lots of options and organizer ideas here. This one is cute!
https://sew4home.com/projects/storag...-vinyl-pockets