Right, we've got a bit of info dumping to do before we can get to the meat of this. Back in March, we reported that The Bear Season 4 had been shot alongside Season 3. Then it was revealed that this wasn't true, until Ebon Moss-Bachrach then said he'd filmed 18 episodes when they'd shot Season 3, which makes one think maybe Season 4 was shot alongside it.
It now seems that the majority of work on Season 4 was done alongside Season 3, and in an interview with Collider, FX boss John Landgraf revealed that there is still work to be done, but it's not much.
"Out of twenty episodes, they shot about sixteen and a half," he said. "So they can go back in production in February to finish."
This still puts the show on track for a Summer 2025 release, even if production starts back up in February. With only a few episodes left to go, this hopefully shouldn't take too long, but it seems this is the way major TV shows suffer from success. The actors become megastars, and squeezing them back into production can be a scheduling nightmare.