Your run space is great. No issues. Maybe add a roost or two. If they are roosting, they may just stay on the roost when you show up-problem solved. But, really depends on the chicken.
Sounds like Pepper may have taken on lead role -similar to a rooster, bc no rooster present. When I’ve had an actual rooster begin to show aggression, “pecking” them can help. One particular male needed to be chased by me and my stick. Every time I’d go in, he’d get chased and “pecked” by me. A few days of this…he avoided me. Worked for me. We had one crazy rooster (so beautiful too…really gorgeous), seriously wacky with aggression. I’d use a rebar garden stake in front of me (not to hit the rooster, just as an extension of me) and he’d bite that metal multiple times..fly up at the stake (me) biting, so much that we couldn’t even grab the waterer to freshen it..we’d have to wait for later in the day. So, some chickens are weirdly aggressive. But, yours is a POL (point of lay) pullet, who may settle down with some age.
If there is any other aggression happening, you could look at diet. Increase protein bc that can minimize certain problems. We feed a 20% protein all-flock, limited treats (which is often just wet feed with a few seeds sprinkled on top). We have to provide calcium on the side using oyster shell.
