See Ecnerwal's answer regarding doing your own wiring in a condo. That is a very important point, and if anything goes wrong - even years from now - your insurance won't be happy.
That being said, I'll answer the technical question, which is independent of the type of building.
You have wonderful colored wires in conduit instead of the standard US black/white and black/red/white cables. That has some significant benefits:
- White is always neutral, avoiding a lot of confusion
- Additional colors are available. For example, you can use the same color, and something different from the more common black and red, for travelers in 3-way switches.
The two yellow wires are travelers. With dumb switches, the travelers are functionally identical. With smart switches, there are a number of different possible ways to use wire(s) between the switches. There is no standard.
Based on the diagram and your particular setup, it appears that:
- Brown is Line/Hot, jumpered from another switch. That goes to black on the new switch.
- White is neutral (it is ALWAYS neutral with conduit), so you add a wire to the existing neutral group and connect it to white on the new switch. You may need a new and/or larger wire nut for the white neutral bunch.
- The metal switch box is an automatic ground. If you have other green or bare wires then you should connect them with the new switch's green wire, possibly with a new and/or larger wire nut.
- One yellow wire connects to red and the other connects to blue.
Now here is where it gets a little tricky. With cable wiring, the travelers can be distinguished by color, normally from a choice of black, red and white. The problem here is that you need to know which of the two yellow travelers connects to which screw on the other 3-way switch - the switch you are not replacing. That is because the yellow wire connected to red (Switched Hot) on the new switch needs a jumper wire on the other 3-way switch so that the common wire on the other 3-way switch always has power (or not) based on the new switch. With cables this is easy - you identify one (let's say "black") and connect it to Red on the new switch and at the other 3-way switch you know to connect "black" with a jumper to the common screw. But you can't do that with "both yellow". So some testing with a multimeter is needed to figure out yellow which wire is which.
But in a condo - or more generally, any multi-unit building - you generally can't do your own wiring, unless you are a licensed electrician. This is not because of landlord/tenant issues - that only applies to rentals. It is to ensure the highest level of safety for others in the building. You can certainly check your local rules, but generally speaking multi-unit buildings require licensed electricians to do all work.