I have had this issue come up in a few countries when traveling and there is often not a clearly defined answer. I always just get a tourist visa if I am there short term and just work. I have never had any problems, nobody is going to know what you are doing on your laptop is work related.

As long as you're freelancing in that way - you don't need a permit or a visa.
If you're planning on staying somewhere for much longer - you can always contact the embassy and tell them how your situation looks like. I think in this case they just need to know the source of your income, but nothing more.

I think it all comes down to where you are a legal resident, if I'm not mistaken. If you pay US taxes and collect US benefits then it should be fine using a tourist visa. You only need a work visa to legally work in that country if you also collect employment benefits in said country. This is my understanding at least.

For example, I work for Matt but live in Sweden. When I travel beyond the EU I get a tourist visa, but I still manage the forums abroad (aka work) without getting a working visa.

If you want to stay somewhere for a longer duration (beyond the usual tourist visa) then you may need to apply...but otherwise, I think you're good to go.