For those who truly believe the myth that the name on the headstock means something to a world-class audio engineer, this is for you.
It's a "Smart Size" 29.5" actual Fender Jazz bass out of Japan. Not sure they make them anymore, but they come up used periodically in all the usual places. Unfortunately, Fender Japan never made a production P in "Smart Size", so you are out of luck there. If you are searching you may have better luck searching for "Smart Size", the SS does not stand for Short Scale.
By the way, in Japan scale length is always measured from the nut to the 12th fret and then doubled. That means the 373.5mm scale translates to 14.704" which when when doubled is roughly 29.5" scale.
Superb world-class choices are mentioned in this thread, such as PRS, Alembic, Rob Allen, Gibson, Hofner and many others. Play the bass that fits you and feels good, extends your playing time and maximizes your potential - whichever one that may be.
Never met an engineer or a player yet - that in a blind audio test - could hear a track and call out the scale length.
The name on the headstock might mean a lot to your local producer/engineer, but if the person is world-class with real aspirations, he or she will lunge at the opportunity and the challenge of experimenting with a wide variety of basses. Especially if you are doing your own music. Focus on what brings out the best in your playing, not the name on the headstock. There's the real truth.