Looks like a bacterial infection.
What are the water temps in the tank?
Bowfin tend to get bacterial and fungal infections if water is kept too warm, (especially if they are a northern variant).
Being a temperate species they also need winter cool downs to remain healthy, a Florida variant might only need a drop only into the 60s,
but the type where I lived in WI might require cool down temps into the 50sF,
For my temperate water species, I would put them in a kiddy pool on the floor of an unheated basement in winter where temps would drop to slightly below 50 in the dead of winter, and thennot feed from the end of Dec, thru Jan Feb andante Mar.
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