Congrats! Looks like you're making good progress.
Did you dig holes and set the 2x4's into the ground a ways? Did it end up stable enough for you? Hopefully it did, but if not it would add a lot of rigidity to add "X" bracing on the sides. You can use small stuff like 1x2's for it if you wanted.
What I mean by X bracing is this: the long sides of your trellis have 4 vertical posts; if we number them in order 1 through 4 from one end to the other, then what I'm suggesting is nailing one end of a 1x2 to the top of post #1 and to the bottom of post #2, then adding another 1x2 nailed to the top of post #2 and the bottom of post #1, then repeating that process to put X bracing all around it. I think you'd end up with 6 X's: 2 on each long side, 1 on each short side. Or 8 if you put a couple over the roof as well.
That could well be overkill, I don't know, but you'll make it work. I'm looking forward to the pics of it once it's covered in flora
