3-way switches cannot be tapped
I'm using the constant power that feeds this switch
Um, no. This is an "I need it, therefore it must be there" cognitive bias.
You are expecting the colors on the 3-way switch to reflect the actual job of the wires. Which they never do on 3-way circuits.
The problem is, 3-way switches don't have power! That's why you must physically throw them with force, and can't control them with your phone. (foreshadowing here!)
Or to be more precise, no switch has both "always-hot" and "neutral". Let's look at how 3-way switches are wired. You need always-hot (black) and neutral (white).
Yellow here is the pair of travelers. You notice you've never seen a cable with two yellows? That's because all cables are made with standard colors. And in 3-way circuits, the travelers are designated by the installer based on surprisingly few rules. (NEC 200.7(C) is it).
You also notice that neither switch has both always-hot and neutral going to it (the two you need). Heck, the right side switch does not have either one!
Welcome to the world of 3-ways.
The lesson here is "3-way switches are poison, never tap them". The better lesson is "Never tap any plain switch".
Hold on though. Smart switches to the rescue!
Now don't get too excited. You'll need to do a bit more skilling-up.
But... "smart switches" handle 3-way switching in a very different way. They have a smart switch "master" that actually switches the lamp. And smart switch "remotes" that use either wired or wireless signaling to talk to the master. Power is rearranged so that all smart switches get power all the time (so they do indeed after all have both always-hot and neutral at each switch).
Again, the topology of your wiring will decide which smart switch is workable. However, once you wire all that up, the side-effect will be that there will be power, after all at the spur 3-way switch that you tried to tap. And now you will be able to tap it successfully.