I think the Kelvin similarities are design choices. Hologram Janeway, Chakotay as the previous captain, the history depicted in the holodeck simulations in Kobayashi, all point to the Protostar originating in the Prime Universe, and as @Deks said, we know the show itself takes place in the Prime Universe.
I think it’s just a design choice, as the show draws on something from everything Star Trek that’s come before.
Plus there's nothing that says SF in the prime timeline (that we know and watch right now) couldn't develop same aesthetics and effects like the Kelvin verse.
In fact, the Kelvin verse UFP might NOT be all too much more advanced than the UFP in the prime universe. Sure, scanning the Narada from shuttles would give them clues, to jump start on a few things, but otherwise, it probably wouldn't have amounted to a humongous leap that would make the technology much more advanced.
In fact, for all we know, design aesthetics and effects do not necessarily correspond with how efficient or powerful technology is... so prime verse SF could have had Kelvin-verse designs and effects already up and ready to be used in the 23rd century... but different choices in design and aesthetics were used due to differences in events... otherwise, how POWERFUL or advanced technology is... it could easily be both the Kelvin verse and prime verse UFP's are pretty similar century for century... and I posited earlier that some things (if not most of them) from the Kelvin verse might have ended up 'aligning' with the prime verse anyway... like the early TNG uniform we saw of a temporal agent as a holo copy that Kovach showed dr. Culber when explaining Georgiou's condition in the 32nd century.
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