Do other countries "pay you" to go to grad school?

Since this is GQ and the OP is looking for facts, perhaps something more specific than “those countries” would be helpful in identifying and avoiding the anomalies.

I recommend the OP avoid any countries where tuition wavers are not the norm for those seeking a science PhD.

Yes, IIRC from what my brother said about 2 decades ago - he was in Engineering. Grad School was just like undergrad, in that there were course lists of what was required for a degree (plus - possibly - thesis). You paid tuition. Part-timers could take 1 or more courses a semester.

However, if you were full time and not totally useless, odds are you would get the TA and RA work, that would cover tuition and living expenses (barely)

I knew several teachers who were taking grad course one at a time toward an MA degree. A favourite was the summer renaissance art study course based in Sienna for 6 weeks. They were paying for the courses out of pocket, took one at a time either evenings or summer semester, until they qualified for a non-thesis (or small thesis) MA. School teachers with an MA got paid more, so if you were interested in the material, it was worth it in the long run.

Pretty much any EU country. Tuition waivers are obtainable, and in some schools even the majority - but they cannot be taken for granted like they are in the US.

I went to grad school in the US for purely economic reasons: it was a job.