As someone not in the industry, what exactly does it mean? The band no longer can perform the music? They no longer get royalties? They no longer can profit at all from the music? They no longer have control over where/how it's sold? Or, something else? What exactly is Warner/Bain buying?

It's a bit like an individual person taking the option of receiving a lottery payment in one large lump sum (and nothing else, ever), vs. receiving ongoing monthly/annual payments for some period going into the future. The new owner pays them one big lump sum and then the new owner gets all rights to license the content for things like car commercials on TV, streaming, reissues of box sets, radio, etc. Also for derivative works of all forms and basically whatever the new owner wants to do with it.

They sold the future royalties. "The new deal with Warner Music Group hands over the rights to the official recordings, meaning the label will profit from any further streaming, radio play or album sales."

All of the above. They are probably required to still perform the songs on behalf of Warner Music but that's it. They are free to write more music... Old music is no longer theirs though.

They have an asset that earns regular income. They are selling the asset and forgoing the regular income in exchange for a lump sum from the sale.

For instance if you own a rental property, you get regular income from rent. If you sell the house you get a lump sum and no longer get any rent.

In this case the asset is musical recordings.