240 VAC power over ethernet?
Stay (the hell) away from feeding 240 V into a Cat 6 Ethernet cable.
These cables aren't isolated for such voltages – it would definitely be liable to hurt someone, or jump through isolation and start a fire. And it would clearly be your fault then.
Really, PoE is what you want. It's literally designed to do what you need. Also &quot;Cat 6, however […] not rated for PoE&quot;: Guess what, PoE will work nevertheless. How you could get the impression it's rated for 230 V instead is a bit confusing, but I think you'll understand that directly feeding in 230 V is not an option.
There's so-called PoE injectors (for single cables, that's a small device you hook into your Ethernet cable, but in your use case, you probably want to simply buy an Ethernet switch that integrates that) to get the power on the cable, and &quot;PoE splitters&quot; to get it out. Some of these allow you to set a desired output voltage (e.g. 9 V), for others you'll need another step-down converter to convert the variable voltage coming out of your splitter to 9 V.