First off Buttigeig still wins Iowa. Since this scenario is apparently presupposing that either Sanders didn't run or drops out early, Warren beats Buttigeig in New Hampshire.
Biden wins Nevada and South Carolina, and goes on to win the nomination fairly easily from there (Warren probably only is a lock to win Massachusetts, while Biden wins pretty much everything else...though if Buttigeig is still in the race when Indiana votes he might win that primary.)
As for rhetoric, I'd expect Warren to essentially be a hybrid of Sanders and Clinton (especially after Harris/Gillibrand/Gabbard/Klobuchar drop out.)
Wait what? Where are you getting the idea that this scenario presupposes any of that from?
I interpreted it to be "just" Biden vs. Warren from the start. So Buttigieg and Sanders wouldn't be involved at all, nor would any of those other candidates.
If that was the case, Biden probably still wins due to stronger black support and probably still stronger support with older/more moderate/rural white voters. But Warren I think had a better chance against him head-to-head than Bernie did, regardless of whether it was a two-horse race from the start or the field dwindled down to one. She would have been more broadly acceptable to more of the party. And at her height she was doing very well with college-educated whites in particular.
I think her coalition and appeal would have indeed been something along the lines of a Clinton/Sanders hybrid. It's interesting to see what the split would be like, because it would tell us a lot about how much the 2016 primary was about cultural/identity issues vs. ideology/policy. If the "Bernie Bros" from 2016 become "Biden Bros," that strongly suggests sex is a major issue. If most of the Bernie people side with Warren, that suggests it's really more about the progressive movement. Likewise with Clinton 2016 supporters, if most go to Biden, it's probably because they prefer more moderate policy. If more go to Warren, maybe they just want a woman president.
In reality we probably would have seen a mix. As a result, I actually could imagine a fairly even split between both Bernie and Hillary 2016 camps in who they went to in this election. Warren's base likely would be diehard progressives, college-educated whites (especially women), younger people, maybe more urbanite types. Biden's would likely be black voters, working class and rural whites (especially men), older voters, and moderates/establishment loyalists. So yeah, that would be a mix of the 2016 coalitions with a significant amount of crossover on all sides.
I think the wild card here might be Latino voters -- would Biden be relatively weak with them as he was against Bernie? Or would they prefer him to Warren? Let's just say that Warren has an edge with them. In that case she could win Nevada, probably also after winning New Hampshire, setting the stage for another potentially drawn out two-horse primary like 2008 and 2016.
