Broadly something resembling the 1950s, with obvious adjustments for the times (specifically on race matters). In other words, two big tent parties with the GOP broadly representing a sort of "measured conservatism" that doesn't rely TOO heavily on nativism, and the Democratic Party broadly representing a redistribution-minded coalition. Some notable changes would be not having any one party region like the South and no Cold War to take center stage.
From everything I have studied, our democratic republic functions best when our two parties represent outlooks rather than a specific set of policy ideas, set in stone. This allows various initiatives that garner enough bipartisan support to succeed (e.g., the Civil Rights Act).
Broadly speaking, what would the electoral map look like under this system? I would imagine that like in the second half of the 20th century most states would potentially be swing states (although each party would retain some strongholds) and there would be much more ticket-splitting at the state and congressional level.
Very hard to say. Places like, say, Lake County, IL that used to vote for Republicans don't so much seem to be bringing their exact set of views into the Democratic Party but rather
adapting their views to fit in with "the new team." In other words, they're not really split-ticket voting that much or anything, and they're largely okay with a Democratic economic message that hasn't really moved right at all, even with an influx of former Republicans. Similarly, despite all the Hawley drooling and stuff like that, former Democrats who've flocked to the GOP are marching lockstep with a Trump campaign that is promoting traditional right-wing policies. What this says to me is that we are so divided that people would rather shift their views a little to remain opposed to "the bad side" than be swing voters in many cases.
I suppose if I tried to imagine it in like twenty years or something, though, it would result in "Whites without a college degree" AND "Whites without a college degree" being about 55/45 GOP-leaning groups (remember, several Boomer voters would have died off by this point, and a very large chunk of this group would be Millennials), with where they live (city/inner-suburb vs. outer suburb/exurban/rural) being a deciding factor, not so much due to cultural things but due to the economic needs of those communities.
It's way too hard to predict a map, but I would like states like Arkansas (large "WWC" population, a lot of conservative voters, decent Black population) on one hand and Minnesota (decent "labor" tradition, traditionally conservative suburbs, traditionally liberal city, swing voters throughout) on the other to be the main battlegrounds. A state like Kansas (ancestrally Republican with a huge chunk of votes in relatively affluent suburbs) should not be anything but reliably Republican with a functioning center-right party, and a state like Mississippi (large Black population, large "WWC" population, a lot of conservative voters) should really be within reach for a Democrat winning comfortably nationally.
