Other than the basic fact that it features an interstellar war, I can't say I think there's much similarity with the Dominion War arc.
There are some others, but I don’t think it outright is a thing. I was just simplifying down. DSC is already ENT like too (first ship of its kind with a certain drive, pre TOS but tying closer in places to post TOS)
In terms of the Dominion war, we have something like a First Contact scenario gone wrong leading to war, the potential for doppelgängers as spies in the main cast, the prisoner of war episode, a...business man of dubious intent declaring it not his war, the musings on the Federation civilisation as a veneer, the motivation of the enemy being one that distrusts overtures of peace as hiding a colonial mindset, the enemy having certain technological advantages, the bending and breaking of rules to ensure certain outcomes, Eugenics enhanced Federation citizens as a part of that, we see infighting among the enemy...Battlefield romance, something like one with elements of an abusive side (odo and the female changeling) ...some of these things are a given for a Trek war story, but it doesn’t change the fact that they are reminiscent of things we have had before.
Do I think it’s intentional or even as deep as that? No.
But if the second half goes ‘trying to find their way home’ then we have Voyagers core premise wrapped in there as well, and Ash could end up being a riff on Seska, or L’Rell could also.
Do I have a problem with any of that? No.
But you can bet I won’t be the only one noticing it.