The role of labor secretary is to enforce labor law, manage some pensions, and do a shit ton of data collection, not to say, run programs that aim to increase unionization rates.

It could be the later, but there's nothing really gained by being labor secretary in that case, Bernie was already engaged in those struggles as a Senator. Bernie as labor secretary could dedicate resources to go more aggressively after violations done by specific companies, but even then Biden could just shut that down.