Wow, thanks for all that input

That array looks good. Only the max. Vds is a bit low for my taste. Totally OK if you're stay with the 12V LEDs. But many higher power are using 24V.
So far I didn't consider support for 24 V strips. But a quick look resulted in the DMN3018SSD-13, which is only a few cents more expensive. So I might just go for that one. Also, the DC-to-DC regulator I planned on using goes up to 28 V, so nothing else would have to change for 24 V support.
The resistor is not required. As this devices are used for USB and they don't allow such resistor especially as it reduces the speed you can archive. But if the 1k (which is much too high IMHO) gives trouble with the datarate you still can still reduce the resistance, even down to 0. From my point of view I'm happy that my ESP reaches the 115kBit. Going to lower speeds start to get annoying. You can do a bit of math here: Check the input capacitance of the ESP, adding some pF for the PCB and calculate the RC-time. Compare the result with the frequency of the datarate.
To be honest: I have no idea whether that resistor would work. I have seen suggestions of 100-1000 Ohms for digital input lines, so I thought I might just try it and reduce the resistance if it caused problems.
High frequency stuff is an area I haven't really looked into so far. So I really have no clue how to calculate what kind of datarate would be attainable (and it doesn't help that I can't find any info on the ESP's input capacitance). Do you know some good, easy to understand introductionary material?
I just noticed: Your power estimation states 40mA for one or two status LEDs. Don't! They're just to bright. Depending on the type, less than a mA is enough and allows you to still look at the board for measurements without sunglasses.
Don't worry, I don't plan to add a small sun to my circuit

I just added that value as a very conservative upper boundary on the power consumption. When I pick the LED I'll take one that is visible when one pays attention, but not more.
What's the reason for using the lower 12 outputs of the PCA? Sure that's no problem, just curious. And maybe you should add a LED to one of the unused outputs of the PCA to help coding without the LED-stripes attached.
I don't really remember. Probably because that looked best on my first attempts with the PCB layout. When I'll make the final PCB layout (once I have picked a case), then I'll assign the pins so that it's easiest to layout.
During coding I just attach my oscilloscope so I can see the duty cycles. That worked quite well so far. That's also why one of the unused pins of the PCA is constantly set to a 50% duty cycle, so I always have a good signal for triggering.
I's probably a good idea to add some decoupling caps to the regulator too. First you should select a type of regulator and then look what are the requirements. Some won't work well if too low ESRs are attached, others require close-by caps, ...
I think I'll pick the R-78E3.3-1.0. It's small and cheap. I'll add 10uF bypass caps on both sides, as suggested in the datasheet.
The power-connector you're intend to use is it usable for 12Amps? And adding some caps on the 12V line won't hurt.
I never intended to go up to 144 W power consumption. So far I planned with 36 W maximum, freely distributable between three strips (including using the whole 36 W for one single strip).
But if it doesn't drive up costs too much, I might as well use a beefy power connector (and use wider traces on the PCB).
About the caps: I thought I'd "reuse" the 10uF bypass caps I'll add for the DC converter for that purpose, as I'll most probably place the DC converter nearby the power supply connector. Do you think that would be OK, or would another 10 or 100 uF cap be better?
Again, thanks for all your input so far!