So, I’m sure this seems to be a repeated ask, but I haven’t seen the exact use-case here yet. I have a Carrier System with 2 stage heating (heat pump + heat strips). They only use the one W2 wire for heating it seems, but upstream, it’s wired together in the furnace unit to control W2, W3, and E. ! am curious if it would be necessary to separate the E wire in the diagram and have it sent to the thermostat for emergency heat controlling, since the Wyze doesn’t seem to be able to control the unit as is (and if I should be concerned about the power not making it to E if wired that way). The honeywell it replaced did fine with triggering second stage heating, but with the last cold-snap that came through last month (Texas) it basically ran almost all day just to keep the house up to temp.
If you wanted Emergency heat on the wyze, you could just split the W wire at the thermostat and send it to both * and to W. (You’d have to reset your wyze and tell wyze your “old thermostat” has a wire at E and W2) There’s no need to split out the E wire separately at the air handler. Alternatively, if you ever needed to run it in emergency mode, you could temporarily disconnect the Y and O wires from the thermostat, which would do the same thing.