Unfortunately, manufacturers are notorious for wildly exaggerating the number of birds that can be housed in their coops, often using the legal maximums for commercially-kept chickens (which are managed with intensive methods not suited for backyard chicken keepers).
The generally-accepted guidelines for backyard chickens are as follows:
4 square feet of space in the coop per adult, standard-sized chicken.
10 square feet of space in the run per adult, standard-sized chicken.
1 linear foot of roost per adult, standard-sized chicken.
1 square foot of permanent, 24/7/365 ventilation per adult, standard-sized chicken.
Because chickens can't read those are guidelines rather than hard-and-fast rules. Some chickens might tolerate tighter quarters. Some might need more space.
The higher the stocking density the more likely you are to have behavioral and/or health problems.