How to connect an AC line filter
There are many different arrangements of Line filters designed for grid input to target device. The above is only a few. Others used cascaded CM chokes with a midpoint filter.
I see a few problems in your setup.

Do not connect green to Neutral. Grn/Yel is always Earth ground.
Do not connect Neutral to your ESD cable on your workbench.
The filter will not do its job if you connect the Grn/Yel Earth Ground wire to Neutral.
Do not use a line filter designed for high voltage lower current to the output of your transformer which is lower voltage, high current. PUT IT ON THE 120Vac ( or 240Vac) side.  But low voltage low current is OK.

My hunch is your 24Vac load was excessive due to the buck converter and caused some resonance with the line filter on your wallwart.
I can only make an experienced guess, because I do not have your measurements or schematics.

Re-wire the filter with a 3 pin plug and socket and add heatshrink to insulate exposed solder joints.

Follow my advice in points  1~5

If you ever notice such voltage loss in future, warning current is excessive and you should use an appropriately rated inline input fuse or PTC ( in an enclosure as it gets hot when activated.)


Conclusion
The Full-Bridge cap DC to  Buck DC-DC regulator caused thermal issues for your brick, possibly exacerbated by the line filter.  The line filter installation info on the web was never searched.
Post Mortem
After looking at the spec link for transformer rated at 20VA 24V , again this must be derated when used with an diode bridge cap load to no more than 15VA.  Then the  DC–DC converter should soft  start and run NO MORE than the same, I conclude you have the wrong transformer VA rating for the job or a bad startup load.
All transformers are rated @ Vout at max VA and expected to drop 10% Vac at this load from no load . When you drop 50% as in your measured voltage, that should have been your clue it was going to smoke. The fine wire primary cannot dissipate the heat fast enough so it is chosen to drop no more than 10% including secondary losses. Thus drawing possibly 5x the rated load dropping another 50% implies your load was the cause of the smoke.  You must verify your design start surge current with sense R’s or ammeter to ensure it has a soft start by adding ICL’s to limit the starting current enable a holding current. These are inexpensive from Digikey.