I'm trying to dynamically set the filter of a logistic storage chest through the circuit network.
I can connect it to the circuit network just fine and read the contents, but I cannot set the filter since the only 'mode of operation' available is 'read contents'.
You cannot set the storage chest filter with the circuit network. It's only possible to manually set one single filter with one single item type.
What you can set with the circuit network is the request "filter" for a requester chest or a buffer chest, so it requests the corresponding items. After all requests have been delivered to the chest, they contain the items that were requested.
As workaround, using buffer chests is probably the thing you're looking for. They request a list of things and at the same time advertise these things as being available in the logistic network. See the graphics in its wiki article: https://wiki.factorio.com/Buffer_chest