Not probably from toenail fungus.
Here is from a good website talking about hot-tub slime, apparently a known thing.
"Biofilm in hot tubs is usually caused by an accumulation of bacteria and microorganisms that exist in the interior or the piping of your hot tub. Biofilm comes mostly from chemicals in or on the body of people bathing, such as skin oils, deodorants, hair products, lotions and perfumes. Older or damaged filters, imbalanced water and ineffective sanitation can also lead to the formation of slime.
"Too much of this slime will reduce the effectiveness of sanitizers, such as chlorine. It can also clog up the piping in your spa, and harbor bacteria colonies."
It basically sounds like toenail fungus from someone who used a hot tub only several times wouldn't be enough to cause slime, and that it is caused by a combo of things that are more normal, such as body lotion.
You might google "how to get rid of hot tub slime."