They have traditional strong ties to one subset of the unions, the LO ones. But it's complex: LO is often openly critical of the (ruling) Social Democratic Party. At the same time a large chunk of the actual union members are voting for a different party, often one in opposition to the Social Democrats.

Yeah, my experiences with Swedish unions is definitely a bit dated, but I guess SD's growth is messing things up a bit, especially in LO?

It is. The LO union members are the ones with the most to loose with a workforce surplus that comes with more immigration (really refugee asylum, traditional immigration is on about the same levels as ever). The Alliance (center-right, when it existed) recogniced this and made the traditionally left humanitarian stance their own. This backfired in a spectacular way when the alt-right wave swept the world. SD takes voters from both blocks.