Can't do it
Here's the problem. Your original installation only has the two wires, even though it controls both light and fan. This means the original switch was not a plain switch. It was a complex beast, which multiplexed both fan and light control onto those two wires.
It can be fairly guessed that it's having a conversation either with a smart fan, or with a fan control module sitting up there in the fan box.
As such, you cannot just slap any random switch in there. You need to use a smart switch capable of speaking the lingua franca of whatever's up in the ceiling. Most likely, that is a proprietary device made by the manufacturer of the fan: the information on the old switch will tell the tale.
Or, gut it and start over
Your other option is to completely gut the old control system, and install a new matched-set of fan control switch + control module (and fan too if the requisite smarts is built into the fan).
Since this appears to use the conduit wiring method, you can semi-easily add additional wires into the pipe if necessary; in principle you could even rollback to the old 3+ wire method of controlling fans + lights.
However, the very fact that you're groping in the dark wondering if a 3-way switch is what you need, tells me that you do not yet have the skills to accomplish such a redesign. If you go this route, I'd either bring in help or skill up.
Otherwise just figure out how to get a compatible switch from the same manufacturer.