What is the resistance of the FPC cable? are R158 and R157 0 Ohm?

I have no idea of the specs of the FPC, the screen is a bought-in module and the manufacturer would not know that spec either. R157 + R158 are the I2C pullups, 4k7.

does it get better if you touch another large electrolytic cap to the 3.3 rail and ground? 10 uF is tiny, so low frequency ( e.g. 50 khz) impedance will be bad

Please show with a photo. How long is your ground lead?

@winny it's the standard ground clip so maybe 80-100mm long, I'm sure you can visualise a standard scope probe without me taking photographs of it for you?

@tobalt I added a 47uF electrolytic on the 3v3 rail and it made almost no difference.

Ok with that new trace, I have another suspicion. Maybe the 3v3 supply does intermittently go into some other regulation mode due to light load. Try increasing the load, e.g. with a 100 Ohm resistor.

100 mm is a problem here. You need a pigtail. See here: e2e.ti.com/blogs_/b/powerhouse/posts/…

Measure common-mode voltage by probing the probe's ground point (so, both contacts to the same point on the circuit). (Use the same length ground clip.) I suspect it is small, but confirmation will be helpful.

@winny just for you I made a pigtail and re-measured it right across the ends of C94 and it made no difference at all to the trace.

Which value is C94, and how far away is the next largest value on the supply net? Note that 10uF at 50kHz is ~0.32Ω so an electrolytic of less ESR is necessary to see any effect. Note also, assuming the measurement is correctly differential, 70mV is not much supply ripple out of 3.3V. Do you know that this is even a problem?

@TimWilliams the scope shows ~15mV common-mode noise when doing that, which is about the background level for the Rigol it would seem.

@TimWilliams C94 was 100nF MLCC, then I added a 10uF MLCC on top of it (stacked 0603's). Adding a 47uF electrolytic across the pads of C94 had no appreciable effect. I can't say for sure this is a problem but the touchscreens are sometimes causing problems (I2C lockups) which is what led me here, and the spikes feel unwelcome at the very least. GT911 specifies <=50mVpp supply ripple so we're borderline.

Good, then you have ruled out measurement error. For future reference, keep the ground lead as short as possible. At high frequencies, this can make a lot of difference.

(To be clear, it's mostly in the 10s of MHz -- "HF" as such -- where probe grounds make a big difference. It would be difficult for this to occur at 50kHz; one would need a serious ground loop elsewhere to do that. Which is still possible, but more obvious to spot, and less likely to happen.)

@TimWilliams Yep, the 1 ms time scale was deterring but some scope (settings) will happily fold over (not sure on the English term here) a HF signal on long time base. Not the case here.

@winny I think it's called aliasing, where a HF signal looks like a much slower one. But I had checked it on a faster time-base before my original post, I just thought the longer view gave a better impression of the overall signal (bursts of noise) rather than a specific capture of the 50Khz waveform.

Can you run an especially low-impedance power+ground twisted pair to the touch screens powers and grounds, to allow any power spikes to choose the lower impedance path you just added?

My comment was deleted. @JohnU Thank you, that was the word I was looking for. From the first image I could not rule it out but with OPs zoomed in one, the 50 kHz was evident. Still strange if it isn’t CM and already fairly strong decoupling.

@MicroservicesOnDDD I really doubt this is about the impedance of the PCB traces, the main rail is 100mils wide copper and there's not only a ground plane but ground pours on the other 3 layers with plenty of via stitching.

My suggestion is not about impedance. It's about changing the path of the majority of the current, to further the process of elimination (to eliminate ground bounce? not sure what we're eliminating yet, just changing one more thing to see what happens).

So far, what you've been trying hasn't worked at all, so it's time to start thinking more outside the box, and trying suggestions that you think won't work.

You can also try adding temporary shielding around the touch screen and its cable, to eliminate electromagnetic coupling from those, either into other parts of the circuit, or into your leads and/or scope. Start eliminating things that sound like they don't make sense. (That is, if you're running out of things that do make sense).