These are my primary suppliers for my hobby projects. I try to order as much from smaller companies rather than Amazon.
https://www.colophonbookarts.com/
My favorite source for linen thread, and other book binding supplies.
https://www.churchpaper.com/book-binding/
They have a page focused on getting book binders short grain paper. They also have reasonable shipping charges.
https://www.thepapermillstore.com/
They have a large supply of paper and some short grain. Their shipping is a bit expensive, so I only order when I have a large order that has free shipping.
They have everything for book binding. I have ordered when I need to, but their shipping costs are high which limits how often I order.
https://www.weaverleathersupply.com/
I have just started ordering from them. I will update as I learn more.
I have ordered some leather from them that was nice, and shipped pretty quick.
https://www.woodworkerssource.com/
I have ordered several sets of lumber from them. I mostly get 3 to 6 boards at a time. I typically get shorter boards like in the 3 to 4 foot length. Basically for smaller projects. Not too bad shipping costs, and lumber is reasonably priced.