How to handle the problem depends on the type of iris you have. These are Siberian Iris; if you have this type of upright, grassy foliage, you have Siberian, or possibly a type of flag iris:

German bearded iris foliage is sword-like; I don't have any pics but easy to find good representations on-line.

I found a photo of one patch - here it is. It looks quite like Siberian?

If only it stayed upright and grass like for a but longer - it would be so useful!

I can't really tell -- it may be a flag iris. I meant to say in my original post that German bearded iris have sword-like foliage. (I corrected the post). I'm not familiar with Dutch iris.

My Siberian iris foliage looks terrific, like what you see in the photo, until about mid-summer. Then it flops terribly. The last few years I've taken to placing plant support hoops around the clumps. It is effort, but it's worth it -- the foliage remains upright all summer and is much easier to cut down in the fall (easier being relative, here -- I find cutting down Siberian iris to be quite an unpleasant chore; if I didn't love the plant so much I wouldn't be bothered with them, but IMO they're worth the effort.

The OP's photo appears to show what are Dutch iris. These are bulbs rather than rhizomes. I've grown them a number of times at different gardens but never did they produce floppy foliage. Typically bulb foliage needs to stay in place until it fades naturally to recharge the bulb and flowers for the following year. Come midsummer, you should be safe to cut them back hard.

If you space them out in clusters like you would do with spring flowering bulbs, they should be less noticeable in a leggy state

Does the foliage of the Dutch iris go dormant?

Yes. As GG said Dutch iris have a corm and Siberian have rhizomes. So it's easy to tell. What did you find when you moved them? Also the texture of the foliage is different and the stems of Siberian are more wiry than the fleshy Dutch. The buds of Siberian are slimmer and enclosed in a dark sheath. But I can't tell that from your picture. Looking at your photo I'm inclined to Siberian but can't really see sufficient detail.

Were the irises as floppy when they were in a large clump before you divided them? I am wondering whether you divided them so much that they just need time to fill in a bit to get denser and stronger foliage.

I have siberian irises (never flop). Love them but due to height and short bloom period (I have 2 varieties so I get 4 weeks of blooms), they are in the middle of my gardens rather than the front. Given the floppiness/short bloom period/height of yours, having them in the front of your garden next to the sidewalk/patio may not be the optimal garden location/position.

They have rhizomes so I guess they are definitely Siberian! The original patch was definitely floppy - a few weeks after flowering they looked like cats had sat in spots all over… and they continue to look the same way once the end of June rolls around. Sigh… what a shame! I wonder if maybe they are getting too many nutrients? I haven’t fertilized in 3 years but I did add topsoil which had some peat moss . I am starting to think I need to bite the bullet and remove them ☹️