Mdd, you are correct about the chofetz chaim’s statements.
However your statement about skver lacks context. Rav nachman’s chief opposition (actually, the only outspoken one i believe) was the Shpoler Zaydeh, which Skver comes from. So they don’t learn rav nachmans seforim in Skver. However, I’ve heard from someone impartial (not a skverer or a breslover) that he was counseling a bochur who remarked to the current skverer rebbe in new square that he was drawn to rav nachman, without knowing that skver is historicallly opposed to breslov. The rebbe didn’t tell him not to learn it.
Most historical machlokes between chasidusen have been settled.