QuoteBards can multiclass freely but if they do the effects of their perk as detailed below are disabled. Whatever song you gained remains in your songbook, however. They may still take levels in prestige classes without losing their perk.
I was building a backup PC as a bard, and noticed I didn't get a song from taking the Perk. So far I've tried it with Skald and Spellsinger on new PCs to check. I wasn't given a songsheet, nothing showed up in the book, and my bard song remained normal for the bonuses and VFX.
When bard perks were enabled again they stopped to grant songs intentionally. At least it's the answer I once got when I had same issue.
Wiki is just not up to date.