Building a Wire Mesh Basket for Under a Table
Here's what I see.  Wire grid from McMaster-Carr.  Brass rod, or steel if you can work with the material competently.  Bend the rod to desired shape on a jig.  Cut the wire grid appropriately then bend it likewise on a jig.  You may need to make the jigs. Then figure out where to put the holes in the rod to take the ends of the grids.  Your call whether to drill the holes not quite through or through and then metalwork the wire ends flush.
For each of the wire ends on the grid, rough it up with #60 sandpaper. We want some surface roughness.
Mix up very slow epoxy with high-density adhesive filler so it's peanut butter consistency, it needs to not leak out. Syringe it into the holes of one of the bars and then carefully fit all the wires into the holes. Make sure all the wires are seated all the way (weight as necessary).  If you drilled the holes all the way through, you can bend excess wire over to make sure it stays where it belongs and work that against spacers/wedges etc. Otherwise feel free to ty-wrap the grid to the bar so it stays put.  Make sure the holes are well packed with epoxy, you only get one shot.
Allow to cure.  At the &quot;stiff enough to not flow but still cuttable with an exacto knife&quot; stage of the curing phase, cut away any excess epoxy.  Don't let it hard cure or else you'll be all day with a Dremel removing it.
Flip it over and do the same to the other side.