It's more complex.
054A (and now likely B) are normal frigates. A lot of independent secondary job (below fleet), (regional, we shall see if 054B will be more global) trade protection duties. They of course can work with squadrons (for that matter, so can 056As, there is no legal prohibition), but from the propulsion choice, we can immediately say it was not the main consideration. The same consideration leads to their consistent 'medium' choice of everything. It's Fleet units that often go to extremes.
054s your stereotypical rank-and-file, do-the-job ships. Arguably, one of the purest of this type in the modern world.
Akizuki/Asahi are fleet escorts first and foremost - i.e. their Chinese equivalent, with a significant caveat, is 052D.
A significant caveat being, 052D is general purpose/multirole(a smaller non-flag 055), when Akizuki are specific AA escorts (ESSM carriers) and Asahi are ASW ones for their "true" guided missile destroyers (mostly tasked with exactly that - carrying task-specific large missiles).
JMSDF has a much firmer work distribution than it's normal for others. That makes them into a bad analogy quite often.
Type 26, are, instead, a RNs main GP combatants - their AA is not even on a proper group protection level (100kg missiles, lol);
they aim for powerful ASW(which everyone readily notices), but also at powerful heavy missile strike (which, for some reason, people miss). Their gun is specifically a specifically DP weapon, too.
If anything, they're almost Russian-styled in their purpose and design: analogies with Russian/Indian vessels are striking.