Hi and help!

[ian]

You should be able to make the structure strong enough

as I mentioned before the key will be accurate tight fitting joints.

However, I'm worried about the stability of the structure
Is it possible to tie the top shelf to the wall one end and long edge?

[TMNT]

What do you mean by backing?

What if I put another cross beam just above the lower rail?

[Christos]

Imagine a frame connected with cross members. When a load is placed on top and a force is placed against the side of that load will the frame move. One way to prevent the movement is to add another piece such as a back, this prevents this from moving side to side.

[ian]

What do you mean by backing?

What if I put another cross beam just above the lower rail?

TMNT
imaging an Ikea bookcase without the shelves.
now add two rails for your clothes.
this would pretty much be the minimum free standing construction that would be kind of stable & even then Ikea would tell you to tie the long edge to a wall and I'd advise you to add a centre shelf taht was fixed to the sides and back.

The critical consideration is the weight of your clothes on the upper hanging rail and the bags you want to store on the top shelf.
the last thing any of us want to hear is that the rack has toppled over with you underneath!