Earlier quoted context omitted.
Do you have work visas for all three countries, or will you lie about your reasons for travel when asked?
Working remotely for your employer (as in, you're not traveling for work, but working while traveling) is not in breach of any tourist visa restrictions.
In reality, you are basically relying on the fact that no one can tell when you open your laptop whether you check personal email or work email etc. But legislation wise you very well might be in breach of visitor conditions. And if you stay long enough, taxes might kick in.
Canada is a notable exemption because IRCC issued a note on What kind of activities are not considered to be “work”?:
> long distance (by telephone or internet) work done by a temporary resident whose employer is outside Canada and who is remunerated from outside Canada;
However, unless the relevant immigrant authority or legislation did this , the law still applies.
There are now numerous countries which issue special digital nomad visas. See https://travel.stackexchange.com/q/45092/4188 for more.