Thinking we'll just scrap the current setup and go for 12V/3S packs with a BMS, and use it to drive 12V LED strip instead. Makes charging easier, gives a much more controllable lighting level, and gives high voltage and low voltage protection to the pack. If we're gonna do it, might as well do it right.
That's not necessarily the "right" way, however. 3s pack ranges from about 9.5V to 12.6V, you can't drive a 12V LED strip with that (unless you are OK with huge brightness variations and basically dismissing the last 10-20% of the battery capacity), it needs regulated voltage, so you either need a SEPIC type converter, or go to at least 4s pack and a buck.
Less complex and more efficient way is to use a proper constant current driver for the LEDs, which is either buck or boost type. You get rid off the series resistor loss in the LED strips.
Unless your LED power requirements are so large that a 3.6V wiring losses become a problem, the boost type has many advantages, like the simplification of the BMS.
Many are available, this is a very typical problem, typical use case is powering backlight LEDs from a single li-ion cell:
https://www.digikey.com/products/en/integrated-circuits-ics/pmic-led-drivers/745?k=&pkeyword=&sv=0&pv1098=408383&sf=0&FV=-8%7C745%2C183%7C337512&quantity=&ColumnSort=0&page=1&stock=1&pageSize=25In practice, this would be 3-4, maybe 5 leds in series per each string (too much voltage boost would drop the efficiency), with a boost-type constant-current LED driver IC driving each string. Such converters typically are approx. 80% efficient, so definitely better than the combination of first regulating the pack down to 12V, then dropping some more in the series resistors to "regulate" LED current.
I recently picked SC4541 because of the integration - the solution area isn't that much more than a simple series resistor! It's a bit more expensive, though, but increased efficiency means savings in battery cell cost.
Pay attention to the LED efficiency, there is huge variation. If you pick a product delivering say 130 lm/W instead of 65 lm/W, you can halve the power and double the runtime. Some random Ebay LED strip may be just 20-30 lm/W.
If you have LEDs everywhere, large total power, and a lot of wiring, then a 4s to 6s pack with local buck-type regulators is more efficient. It should still optimally be a constant-current LED driver so you can skip the series resistors. (If you want to do it "right", that is!)