Doing a quick search on “Yorshik” (Ёршик), of the very few sources I could find on the topic, while the word does seem to translate to “brush” there doesn’t seem to be any surface connection to toilet brush per se, though naturally it may be possible on a colloquial level.
This source that deals with meanings and etymologies of Russian words says:
Слово «ёршик» является диалектным выражением, используемым в русском языке для обозначения маленькой ёлочной игрушки в виде ёлочной ветки или шишки. Это слово имеет древнерусское происхождение и связано с древними славянскими обрядами, связанными с поклонением природе и деревьям.
Which DDG translate says means
The word "brush" is a dialectal expression used in the Russian language to refer to a small Christmas tree toy in the form of a Christmas tree branch or cone. This word is of Old Russian origin and is associated with ancient Slavic rites associated with the worship of nature and trees.
The only other resource I’ve found is this 11 year old YouTube video in Russian, that I can’t really understand. They seem to be joking about something, and “New Year” is mentioned, but I didn’t hear the word for toilet.
As far as I can understand, Yorshik seems to mean “brush” or “little brush”.
“Don’t mind me, just arguing semantics in a discussion about pedophilia. Carry on.”