A few months ago, I wrote a short (informal) note that reviews the general forking lemma and several variations thereof, and discusses the differences among each variant.

I have recently updated this note to include an expanded version of the proof of security for Schnorr signatures. In particular, I included an explicit simulation algorithm (Figure 3) and more detailed explanations for how the bounds are derived (Lemma 7.3).

You can find this expanded proof for Schnorr signatures in Section 7 of the note.

Many thanks to Gregory Neven for his discussion on the steps to derive these bounds from the general forking lemma.