Let It Be came out after the band had already broken up.

Yes. Let It Be was released in May 1970, a month after Paul McCartney publicly announced the breakup in April 1970. The band was already done.

It’s a weird one because the recording sessions actually happened before Abbey Road (late 1968–early 1969), but the project sat on the shelf while they argued over mixes and Phil Spector’s production. By the time it finally dropped, the band had officially split.

So technically it’s the last studio album they released, but not the last one they recorded. That distinction belongs to Abbey Road (September 1969). If you want to get pedantic, Let It Be is the posthumous studio album the Beatles released while still technically existing for a few more weeks.

It’s a messy ending for a band that never did things neatly.