No, that’s a very bad idea. BTRFS has deduplication, without that the snapshots would take up way to much space. Also it’s too many writes since ext4 doesn’t use cow and would have to do distinct writes for every snapshot.
The 240 gb are plenty for a root system without /home and years worth of snapshots on a btrfs volume, only the changes take up space so the amount of snapshots hardly matters.
For /home either ext4, xfs or btrfs is fine. Personally I only use a single btrfs volume and put certain folders in their own subvolumes so they can have different settings for snapshots(no snapshots for /home, tmp and cache folders).