Update: I tried setting init = 1 in $sample() (using cmdstanr) and it looks like it completely solves the problem on my end! The slow chain is easily 20x faster now and keeping up with the other chains.
My only concern is that I do not fully understand what init actually does. (I read the docs but have only an intuitive superficial grasp of what HMC is doing.) I am concerned about the potential consequences of setting init too low (comment: One MCMC chain not moving).