How intense is your pecking order?

[FrostRanger]

You could try to introduce mature, hardy, woody plants in pots to the run. Small trees, berry shrubs, stuff like that. Young plants are easy to destroy, and stuff like strawberries and herbs, chickens will just absolutely shred them within hours or days. Mature tomato plants are great for shade and having dirt baths under, plus they can snack on the tomatoes!
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Raspberry plants are great because the thorns keep the chickens from tearing up the stems. You can kind of braid and shape the stems into a diy shelter! Mulberry bushes are sturdy, great shelter, great roosting and foraging opportunity. We have a few growing wild on the property that the girls routinely pick berries off the ground under.

You can try growing vine plants up the side of the run, like beans, peas, ivy, nasturtium, etc.

Look into native plants that will grow well in your environment too, if you want to go the planting route. Native plants tend to do much better in the long run and are healthier for the environment!

Be mindful mulberry can get very tall, we have one in our driveway and it's probably around 30ft tall and that's evidently on the shorter end of how tall they can get, some can get up to 80ft tall. Ours is unfortunately a male tree so no fruit but it does have nice flowers in spring

My flock made up of 3 easter eggers, 3 lakeside eggers and a buff orpington (all hens) is pretty peaceful other than normal pecking order stuff. I pretty rarely free range and they have a 12x12 covered run they hang out in. No idea why your flock is so high strung, some flocks are just like that unfortunately, you've been given some pretty good suggestions to hopefully help things

Adding a rooster may or may not help things. For some people adding a rooster completely sorts things out, he keeps things from getting out of hand and breaks up fights, for others a rooster does absolutely nothing, he'll pretty much just ignore the fighting and do his own thing and unfortunately for some the rooster adds his own drama to the mix. Not saying that a good rooster can't help but finding a good rooster that does keep the peace can be an ordeal in of itself. Personally, unless you already want or need a rooster I wouldn't get a rooster hoping he'll solve the problem, he might or he might cause more drama himself

 

[ValkerieGunn]

My Bantam Cochins sorted themselves out early and once introduced to the rest of the flock who free range they stay near the older hens who normally stay around the back of the yard while the rest of the spring babies have claimed the front yard. Although my 2 Bantam Cochin cockerals are definitely in charge and putting the other larger cockerals in their place until I figure out who is staying or going.