It's great to see realistic photos of regular flower beds! Most of us don't use a gardening service to create or maintain our beds, so our gardening chores get balanced against other activities. Voila, instant real garden!
Usually when I see stacked fan leaves it is right before the fan is ready to split into two new fans. Here's a "before" picture of a cultivar that bent itself into a "V" shape and is now become two distinct fans. I'll try to get an "after" picture tomorrow when the sun is up.
When there are both close-in and further-out shoots coming from a fan I think it just means that it has a "mixed" root system. The two main types of roots are short-and-bulbous and long-and-roaming. But, after so many decades of crossing the two older types, it seems like most have a mix of the two. So, some shoots are coming from the main crown while others will pop up from the rhizomes. I haven't check whether fully-rhizome type cultivars also send up close-by shoots (I just can't keep them in the garden to check it), but I suppose that is possible, too.
Short bulbs, Long rhizomes, Mixed Short and Long
I've had some super flop-over fans, and learned that it may just be a sign of heat-related summer dormancy, especially after a scape has bloomed or some other event (like new shoots) has sapped its energy. Yup, they righted themselves, even from this extreme type of flop:
