Hi,
The problem is with the variants of your products.
Either you've manually modified them with mass actions or through the database, or you've imported them with wrong data.
I've created a mass action so that you can see the issue in your backend :
take.ms/Ge6WU
You have the main product set to a warehouse, while you have the variants of that product set to another warehouse. And when you add a product to the cart with variants, it's actually the variants data that is used if it exists.
And in your case, even though you set the main product warehouse to the warehouse with the id 3, you set the variants to the warehouse with the id 1, and thus you see the shipping methods of the warehouse 1 when you have these variants in the cart.
So you need to fix the warehouse data of the variants and it will work properly.
For example, you could process a mass action with a filter on the product_type equal to "variant" and an action "update the values" on the product_warehouse_id column with the value 0.