Our suggested changes to the code base to enable emscripten support: 
https://github.com/aibasel/downward/pull/16

That sounds really cool! :-) Hope someone will find time to look into this in the not too distant future, right now we're all a bit overloaded with teaching and service. So this is just a quick first acknowledgement.

We pushed the necessary changes for running the translator in the browser to the same branch ( https://github.com/aibasel/downward/pull/16 ).
It works by first building the translator as a Python wheel and then running it in the browser using Pyodide.
The code for that (incl. Readme and example files) is in src/javascript/translator.
It is now possible to run both the translator and the search completely in the browser.

I thank Jendrik and Christian for their comments.
We managed to run the translator in the browser using Pyodide. 
After the student who did this has finished writing his Bsc thesis, we can include the necessary changes for running the translator in Pyodide to the Pull request, if you want.

Having a browser-side PDDL parser/grounder would be phenomenal, btw. Not just 
for FD-in-the-browser, but for anything that we'd like to do in the editor 
plugins. Spent the last semester guiding a student team to use the STRIPS npm 
lib, but there are issues with the grammar and scalability bites us 
immediately (naive grounding instead of datalog).

Just wanted to loft my voice on the stack of users that would love to see a 
browser-side parse+ground!

We discussed this today in the Fast Downward meeting and came to the conclusion that running Fast Downward in the browser will only be really interesting if the translator can be run in the browser as well. This could for example be achieved with a Python implementation for the browser (e.g., Brython). There are also plans for converting the translator to C++, but these are very much long-term plans. If you'd like to work on supporting the full planner in the browser, we think it would be best to start with a discussion about the implementation strategy.