specifically Non-Hierarchical Polyamory
As others have noted, you are married, therefore hierarchical. I did a lot of reading when I started out too, and decided I too did not want hierarchy, but quickly learned that is impossible in a marriage, and even in many poly relationships, as well.
There's nothing wrong with hierarchy. The problem is people in hierarchical relationships saying (lying or pretending) that they don't do hierarchy.
What you need to be clear on is HOW and WHAT your hierarchy looks like.
I have a life partner that is the center of my love world. A new partner may or may not become as close to me as that, but the option is there to have a multiple-primary hierarchy. It will take a lot of time, so don't expect equal treatment in a year or two.
However, as I become close with partners, I do make commitments of time, being there in emergencies, and I ALWAYS make my own decisions regarding my relationships. NOBODY has power in a relationship they are not in, so there's no vetoes, and I have complete autonomy in my relationships. I may not be able to give everyone the time they want, but I spell it out and make it clear what I can and cannot give, so partners can have full consent or decide it's not the relationship for them.
For me, I don't see hierarchy as 1, 2, 3, where only one person can hold that top spot. I see it more like orbits, where anyone can become close enough to reach any orbit and can freely move from orbit to orbit. My top orbit currently consists of my life partner, my best friends (yes, I have more than one best friend), my father and my nesting partner. My second orbit is very close family and other partner. My third orbit is less close family, friends, newer partners or comet partners. My 4th orbit is new dates, friends/aquaintenences, distant family, colleagues, old schoolmates, etc., and the 5th tier is the general public.
That top tier is reserved for the best possible relationships. For me, romantic partners would have a hard time getting there... It's only happened twice in my life. Love is not enough to get to my top tier.
So, rethink how you want to express your hierarchy, own it, and make sure all partners understand it.
I've seen couples try so hard to not have hierarchy that they neglect and even harm their committed partner so as not to appear to give special treatment, and actually winding up giving that special treatment to new partners instead.