Warning! In the process of this experiment, you most possibly have created some amount of toxic, carcinogenic, and environmentally harmful waste. Read further for answer to your question and more details.
All the nasty buildup is probably composed of carbon that was originally in the steel, mixed with some amounts of insoluble oxides and/or hydroxides of steel's constituting metals.
Stainless steel is a particularly bad choice for an electrolytic anode, because it contains chromium (at least 11%, often much more) and nickel. Both nickel metal and soluble nickel salts are toxic and carcinogenic. Chromium gets mobilized into the solution by being oxidized to trivalent $\text{Cr}^{3+}$ ions which, under favourable conditions, could get oxidized further to especially toxic and carcinogenic hexavalent forms $\text{CrO}_4^{2-}$ and $\text{Cr}_{2}\text{O}_{7}^{2-}$ (chromate and dichromate anions). It is absolutely unacceptable and illegal to dispose of such waste by pouring it down the drain. If EPA knew about any such incident, they would be on that person like flies on fresh manure.
From https://www.sciencedirect.com/science/article/abs/pii/S0360319920301403 (the article uses $\text{Cr}^{6+}$ for hexavalent chromium -- no such cation exists in standalone form, though; it is just a convenient way of denoting $\text{CrO}_4^{2-}$ and $\text{Cr}_{2}\text{O}_{7}^{2-}$):
Alkaline water electrolysis is one of the easiest methods used to produce hydrogen, offering the advantages of simplicity and low cost. [...] Stainless steel (SS) is considered one of the least expensive electrode materials for alkaline electrolysers, since it is relatively chemically stable and has a low overpotential. Nevertheless, SS anodes do not withstand high concentration alkaline solutions because they undergo a corrosion process. If the electrolyser operates at a voltage of up to 1.6 V, it can generate Fe3O4 and hazardous hexavalent chromium (Cr6+) at the anode. Hexavalent chromium is generated when the chromium-containing stainless steel electrodes undergo an electro-oxidation process.
In order to neutralize any potential hexavalent chromium you need to add a large amount of reducing agent, such as sodium thiosulfate -- it will reduce the toxic and carcinogenic hexavalent chromium to the less harmful trivalent. Nonetheless, while much less dangerous, trivalent chromium is still somewhat toxic and cannot be poured down the drain; not only that, but nickel still remains a problem.
Pour your waste into robust plastic containers, like those white, one gallon "jugs" in which household bleach is sold, and clearly label them as hazardous. From then on, you can pay a chemical waste company to have this waste disposed of for you, or you can store them in some safe and isolated place where absolutely no children or animals have access to, until you can have them properly disposed of.
PS If someone spells "chromium" as "chrome", or claims that any amounts of sodium could be obtained in aqueous electrolysis, I would highly suggest against taking any advice from such a person.