He’s also coming to the realization that if their trip home takes as long as predicted it’s likely that he will be Captain by journey’s end. First and second are adults humans in their 40’s and he’s got plenty of years left on him as a Vulcan. It’s unlikely that Janeway or Chakotay won’t be too old to really do the job in 50/60 years time.
He can’t afford to just be a security officer, he needs to start thinking about command and the additional skills he must develop to become Captain in every sense. That means adjusting to the differences in the way the two jobs are concerned with personnel and mental well-being. Captain is more than just the ability to take charge in a combat situation and be successful, but the long term devotion to crew and ship on a personal/loyalty level which Tuvok doesn’t display in the early seasons. He’s far too pragmatic for it, additionally he distances from personal relationships which a Captain must have with their department heads.