Power injection works, but doesn't work well

You are asking a lot of the data wire from the end of the 1st strip to the start of the 2nd, that’s on the long side for a data wire (any data wire).

The bigger issue is your injection line.

Your strips are 60 LEDs/m guessing .3W/LED at max brightness gives 18W/m of strip (max).
Guessing your end strip is 2m(?) gives 36W or at 5V that’s a little better than 7A (max).

Refer to one of the voltage drop calculators: Voltage Drop Calculator
Plug in 10m at 5V and 7A for 22AWG wire and you get?

A voltage drop of 7.47V or 147% of 5V or you won’t get anything at the LEDs it’s all lost as heat in the wire.
But, you say I don’t need max brightness, 50% will do fine!
Plug in for 3.5A and get ->3.7V drop, so a whopping 1.3V actually gets to the LED’s
Go to 25% brightness, 1.75A → 1.85V drop leaving only 3.15V for the strip.

You’re asking your injection ling to carry too much load over too long a distance with too small a wire.
22AWG is fine for data, but is not suitable for the kind of current you’re asking it to carry.

You may still need to deal with the length of your final data line (I always suggest a TxRx differential pair at 10m), but realistically until you deal with the power issue data is moot anyways.

BTW, your power supply is likely just fine.

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