The L1 Pro is a destination, not a source. Your Bluetooth music is going to the L1 Pro, and your vocal into the T4S is going to the L1 Pro. The L1 Pro plays whatever it receives, i.e., both the Bluetooth and your vocal, but does not send anythingback to the T4S (i.e., the Bluetooth music.) Your vocal (the only thing passing through the T4S) is going to Audacity on the laptop via the USB connection.
To accomplish what I think you're trying to do, you'll need to send your music to the T4S directly, instead of to the L1 Pro. You would use a 1/8" TRS to two 1/4" TS Y-cable (preferred for quality sound) or to a Bluetooth receiver connected to the T4S. Then you would send your mixed signal to the L1 Pro via your cable AND to Audacity on your laptop via USB.
Another alternative would be to record to the laptop from the LINE OUT on your L1 Pro. This would involve different cables, possibly additional equipment, and changing your equipment around.