They've let people in with just a currently valid Danish driver's license before, but I suggest using documentation that is accepted by the Swedish police as proof of ID and citizenship. Currently, no evidence of vaccination legally required by Sweden for people coming into Sweden directly from Denmark with Swedish-accepted ID; and it seems like Sweden won't be going back on that anytime soon.

Every person I've seen the Swedish police removed by train from Sweden to Denmark -- including within the past 60 minutes -- this week has been someone who appears to be of non-Nordic/non-Scandinavian background. I've only seen men removed during the last several days; and at that it's been people who come across as being from central/eastern/southern Europe, or, less commonly, from beyond Europe.

No border control checks right now if coming into Sweden by train from Denmark.