Quick disclaimer that I’m not an electrician, your wiring might be unusual and there is a chance my understanding of all this is 100% wrong anyway . But I got one to work on a 3-way fixture I have by installing in the ceiling with help from others on this forum. You need a basic understanding of home electricity and probably how to use a multimeter too. Sharing pics of your wiring helps.
If you don’t have a neutral wire in your wall switch box, then it has to be up in the fixture box. By convention it’s the white one, but you do need to check with a multimeter. The diagram below is likely what you have.
Use the diagrams in @johnconstantelo’s post to understand how to wire your hot and neutral to the aeon micro switch, you may need extra lengths of wire and wirenut them together. The two wires that were coming from your switch can be connected to the switch terminals on the aeon switch. That should take some extra wire and wirenuts too because those switch terminals only take 18G wire.
Your outlets can be controlled with either a plug-in switch device, or you can replace the receptacle with a connected outlet, there are several manufacturers that make both.