What would be the Western / American equivalent of the Troyka Shield and modules?
This probably has no complete, general solution.

The Troyka Shield looks to be just a prototype shield with footprints for ground/power/data cables.  Likely you can just use a different mechanism to connect things, solder some additions to an everyday proto shield, or you could relatively quickly duplicate this in a PCB design program and have boards made.

There are probably many alternatives for the mechanical structure, ranging from cardboard and foam tape or hot glue to various toy building block sets, or you could try to duplicate their idea by making some grids on an everyday 3D printer.  Likely none of these satisfy formal ESD concerns - but then, Arduino projects are usually considered disposable enought that people rarely worry about this.

The modules are going to be the most problematic part.  They seem to encompass many of the peripheral parts and chips usually used in Arduino projects, and most of those are already available in canonical modules from a range of vendors like Adafruit, Sparkfun, Seeed, etc on down to clones and simple executions of chipmaker's recommended circuits.  So for most of these, you'll probably have no problem finding a substitute, the possible complication is if you have enough understanding of the details of each assignment to make any necessary changes to accommodate for differences in pinouts, components values, etc between the specified Troyka module and the chosen substitute.

You may in the end find it's better to just follow tutorials written around the specific parts and modules you find more readily available for purchase, and thus avoid the needs to translate the details.

Do beware however, that there are some really bad tutorials out there on the Internet - some in places like Instructibles are simply terrible engineering to the point where it is a minor miracle if they even worked once for their authors, and even some on the Arduino site cut corners in ways that can't be recommended.