The .ass files are generated based off whatever telemetry types are being shown in QGC’c telemetry widget during operation. From the available fields it doesn’t look like there’s one for visual odometry (which is what the DVL extension presents itself with to ArduSub), and the position ones look to be specifically for Gps messages rather than the vehicle’s position estimate, so I don’t believe it’s currently possible for QGC to put DVL things into its .ass subtitle files.
The vehicle has internal DataFlash .bin log files, and QGroundControl also logs the MAVLink messages it receives during operation in .log telemetry logs, which can both be parsed using Log Viewer or programs like Pymavlink’s mavlogdump.py.
If you’re using .bin logs the VIS* messages give you the information ArduSub is receiving from the DVL extension, and the POS messages log the vehicle’s position estimate from ArduSub’s sensor fusion (its EKF). In .log files you can look at the GLOBAL_POSITION_INT message data, and possibly also any VISION_* messages that get passed along.