The most stable joint for this in wood would be a Mortise & Tenon joint. Making this joint is reasonably easy if you have some tools like a table saw and some chisels and/or a mortising attachment for a drill press (pillar drill in British). You can make them entirely with hand tools - a simple cross-cut saw and a chisel and hammer/mallet were all that was necessary for many centuries before all the power tools were invented.
Normally, stands like this will have 3 legs in a triangle as you've drawn because that's a very stable design requiring a minimum of material. However, since you're working with a square post, having 3 legs would require that 2 of them go into corners of your posts and that will make things more difficult. I'd suggest using 4 legs, simply because it will make the work easier.
Make your mortises at an angle in your posts, I'd suggest that you have 2 on opposite faces at one level, and the other 2 on the other faces at a different level. This will make it easier to make the interior joint spaces and, more importantly, will give more strength and stability to each joint. Cut your legs at a matching angle and cut the tenons to fit.
If you have well made, snug fitting joints, you should be able to pull them apart for storage and knock them back in place when you need to set it back up. Glue, obviously, will prevent you from taking it apart, so don't glue it.
Since this will take some precise joints, I'd suggest that you do some practice M&T joints to improve your skill set before tackling the real project. It's not difficult, but you'll want some practice before digging into your full-size lumber.
I'd suggest that you visit the woodworking sister site for any specific questions you may run into while making your M&T joints. There's a lot of knowledge and expertise there to guide you through the process.
All that said, I'd really suggest that you pick up some pre-built aluminum stands. Considering that the backdrops were free, the investment in the stands would be a reasonably small cost in comparison. They'll also be lighter to move, fold and store easily, and be easier to transport.
I'm all for DIY and woodworking, but sometimes, it's easier to get something that's designed for the purpose.