Let me use these labels in this answer:
- A: あれは彼のだよ。(の as のもの)
- B: 赤いのが欲しい。こんなのが欲しい。(の as もの)
- C: 絵を描くのが好きだ。(の as a nominalizer)
- D: 彼女は学生なのだ。彼は知っているのだ。(explanatory-の)
準体助詞 is not really a widely used term. According to the following links, 準体助詞 can be roughly summarized as "a word which was originally a 助詞 but has gained the role as a (形式)名詞". Some people believe it's still a special 助詞, and some people believe it's effectively a (形式)名詞 (or a suffix) already.
名詞 on Wikipedia says C is 準体助詞, and says it's called so because it was originally a 助詞.
助詞 on Wikipedia says C is categorized as 格助詞 by some.
準体助詞 on デジタル大辞泉 says A, B and C are 準体助詞. (But its definition contains ～とする, implying this is not a universally accepted concept.)
準体助詞 on 精選版日本国語大辞典 says A is 準体助詞, but also says many believe it's just a noun.
の and のだ on デジタル大辞泉 say A, B, C and D are all 準体助詞.
の and のだ on 精選版日本国語大辞典 say A is "格助詞(準体助詞とする説もある)", B and C are just 名詞, and D is 格助詞.
の on 明鏡国語辞典第3版 explains A, B, C and D under 助詞, but without using the term 準体助詞 itself.
Many Wikipedia articles acknowledge C and D are 準体助詞. See these search results.
Several websites for JSL learners I checked treat の simply as a 形式名詞.
So all of A, B, C and D might be called (準体)助詞 depending on the writer's preference :)
I personally think の in B, C and D can be simply explained as a (形式)名詞. の in A is somewhat grammatically special, but it can be explained as a noun-forming suffix, too. Practically speaking, the etymology-based category, 準体助詞, seems not very useful to me. From the standpoint of a modern Japanese speaker, I can think of no practical merit in thiking 寝るのが好き and 寝ることが好き are syntactically different, even if this の was etymologically a genitive particle.
(By the way, I personally didn't know の-as-a-nominalizer derived from the genitive case particle の. It's semantically much closer to こと/もの now...)