Very much the same thoughts here. It seems to me like they had another go at Enterprise and did it well this time.
To answer the poll, DS9 is my favourite series, and I'm enjoying DSC.
The things I liked about Deep Space Nine are definitely similar things that I like about Discovery, so I would accept the premise that there is crossover there. It isn't about 'darkness' or 'grittiness', it is about complexity, about difficult storylines without easy answers, its about space feeling dangerous and exciting again, its about minority and female characters with agency and strength of character, its about relationships that seem natural and human, its about characters with interesting backgrounds that actually affect their character in the present, its about consequences, growth, progress and following through with ideas.
DSC's first season strongly reminds me of DS9s, in a number of ways. It's still got a bit of clunkiness to it, it's got some missteps and ideas that didn't work as well in the telling as in the conception, but it has a set of characters which fascinate me, that I want to see more of, that have room for growth and whose actions affect them and others around them. It isn't afraid to address complex issues head on. It already feels like a big universe with a lot going on, with a supporting cast that are worthwhile characters in their own right. Lots of positive parallels there.
I don't know if we'll have a Duet by season's end, but we've got a few In the Hands of the Prophets already.