You've never worked with LEDs before, eh? Think about what you assume about every other electronic device, ever:
- it has a specified amount of voltage it needs
- the device internally controls itself as to how much current it draws
- with multiple devices, you connect them in parallel
- your power supply must deliver correct voltage, with capacity for at least that much current.
All that goes out the window with LEDs. If you give them constant voltage, they explode, because they can't control themselves. Current must be externally regulated, as in a ballast, except they call it a driver. The correct current may occur at a range of voltages, but not too wide a range, +/- 15% or so.
Since constant-current is the critical factor, and LEDs are basically indestructible, it is most design-efficient to wire them in series.
Think it through.
This is really different thinking.
The series wiring
Ok it needs constant current, self regulates for voltage, series connection and the power supply must deliver potentially a range of voltages to hit that current.
Ok now the series wiring makes sense: items in series have exactly the same current, so you can control all their currents precisely from one driver.
Now the driver's labeling totally makes sense, the wild range of voltage but the precisely narrow current range. 260ma is the correct current, the end.
Here's what bugs me, with 30LEDs in the outer ring and 24 in the inner, and they're in series, that's 54... Unless they are red, voltage per LED is typically 3 volts, so I'd expect 162V give or take. That's too high for the driver. It's possible inside each ring they are wired in series-parallel in sets of 2 or 3, see if you can easily divine this from the PCB traces, don't wreck it.
That driver is a bucking converter, taking a high voltage and lowering it. From the "printed on a 90's plotter font" markings, and lack of UL/CSA/TUV stamp (CE is not that), this is generic "fell off a truck in Shanghai" Cheese junk, which suggests maybe the lamp is too. I wouldn't put it past our Pacific Rim buddies to use an out-of-spec part. Overvoltage is less damaging than overcurrent, so you can usually get away with it.
So while 260ma is a sure thing, there's a real question as to the practical voltage of this thing, which may impact selection of a driver. I would pursue that further, by putting the smaller ring on a CC/CV bench power supply, setting it for 10ma, turning up the voltage until it starts to light, and turn it off before it overheats without its heat sink. It won't light at all until it's within 20-30% or so of its rated voltage. Running a 260ma LED chip on 10ma is fine, in fact it's the best way to dim them. Whatever voltage you hit is in the ballpark, e.g. If it's 60V (2.5V per LED) that would indicate they are all in series and all 3V devices as expected.
If the inner ring is all in series, the outer ring will be too.
Selecting that driver
Now you have a definite current (260ma) and a rough range of voltage (162V or 81V or whatever you found). Go shopping and find your driver. You might find that exact driver on AliExpress (Cheese junk supermall) but I would aim for a better vendor, especially if the voltage was out of spec. I would try electronics shops like Muser or Digi-Key. Read data sheets carefully.