I’d say here the biodegradation isn’t a concern. Biodegradation is a concern for things that might get accidentally thrown around by wind. An example: if you are generally an environmentally friendly person, you could still use plastic bags and the wind can “steal” your plastic bag with you being unable to retrieve back. Then, the plastic bag becomes microplastics in the oceans, even though you didn’t intend that to happen.
Since you are asking about this, I’d say you are not the kind of person that throws toothbrushes into the environment.
Just ensure your toothbrush is properly handled during the end of its life — burnt to carbon dioxide and water in a waste-to-energy facility — and you are being very environmentally friendly.
Toothbrushes contain so little plastic that whatever plastic they have I’m sure will eventually be made from trees or from captured carbon dioxide and hydrogen. Today it’s made from oil, so burning the waste toothbrush into energy increases the atmospheric CO2 concentration but only so little that it doesn’t matter.
