This mod: https://mods.factorio.com/mod/paste-logistic-settings

Will let you copy/paste assembler product into the "Logistic filter" slot of Storage Chests.

Your mod will let you copy/paste assembler output into an Inserter and it will create a green wire connection to a metal chest and set the inserter stack size limitation.

Some issues:

1) Your mod does not perform the same operation on a Storage Chest as it does on metal chests (it does not add the wire, but it does somehow set an operability condition--seemingly a bug)

2) With both mods enabled, the functionality of Paste Logistic Settings is broken. That is fine! but it would be nice if you could do the same thing as that mod wherein: pasting from an assembler into an Inserter facing a storage chest will do 3 things
(a) create the green wire connection to the Storage Chest
(b) set the operability condition on the inserter and
(c) set the Storage Chest filter to be the product of the assembler.

1) that's not a bug. It sets a Logistic Network limit when you paste to an inserter that's facing a logistic container. However, I can see how this might be useful, so I've added an option in 0.0.4 that lets you select which behavior you'd prefer
2a) see #1
2b) see #1
3c) I've also added this. If you paste to an inserter facing a storage chest, it will set the filter for that chest. In the event that there are more than 1 products it always chooses the first product from the recipe product list.