Stop leak for radiators is water glass, sodium silicate. It is safe to use for a hot tub. Just buy a gallon of water glass from a farm supply store. It is commonly used to seal drinking tanks for cattle. SOME stop leak has powdered aluminium or brass added so you don’t want to use that kind in a hot tub. Sodium silicate hardens to a quartz like substance in the presence of CO2 so you can speed up the process by spraying a can of CO2 on the outside of the tub wherever you see water leaking. I’ve used water glass mixed in sand to make metal casting molds. A quick shot of CO2 hardens the stuff instantly.
Eggs are also coated with water glass to make them last longer since it fills the pores in the shell and keeps air out.
The stuff is incredibly benign.
It won’t seal a huge gap in the staves; cracks are what it seals best.