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First we’d need to define “internet” for this purpose. Does classic mail qualify? It certainly can carry more data than pidgeons, and if you can still have computers you might get relatively close to the 90s internet by sending data by mail (especially when you’re communicating with people within a day’s travel, rather than on the other side of the earth).
Other than that, you can do a lot with visual signals. In the Discworld novels, they developed a kind of optical telegraph network with a technique that is somewhat similar to ship flag communication, and optical telegraphy exists/existed in the real world, too, though it never got much traction. If you have computers, you might be able to get pretty alright data rates with something like that.
I’d assume the taste of soap is usually a lot stronger.