You should know soon whether you like those berries or not. I live next to an abandoned yard that now has several hundred sq ft of berry bramble adjacent to our yard, a shared CL fence. The only problem I have with them is that you can't have just a little. This kind of vine will grow under the soil for various and arbitrary lengths, then pop up, in the lawn, in a shrub, wherever. Mowing isn't necessarily enough to keep it in bounds, little pieces can survive enough to send shoots farther out, until it finds somewhere where it's not being mowed. It's quite different from a ground-cover type plant that creeps out in a visible, widening circle, because of the impossibility of knowing where it's gone, invisibly. Having any in close proximity greatly increases your chances for seedlings. Those are easy to pull, but regular monitoring is necessary to ensure you find them while the whole thing will still come up. Gardenia should have the main bloom soon, shouldn't impede your access to the berries and the vines look like they are using it for support. I might recommend enjoying the flowers, likely on while you pick berries, then addressing each plant as you see fit. I know nothing about store-bought raspberry plants, my comments are not in regard to them at all.

I agree that it is a Gesneriad, specifically, some species/variety of Aeschynanthus, aka Lipstick Plant.

Yes, it definintely is a cane begonia. Thanks! The flower is a little different than the one on the link you provided, but I'll do some more research and see if I can find it.

Just wanted to mention that the flowers look like they'll be "umbrel" shaped when they bloom, and add a pic