This recipe is listed under the section for fermentation, together with beer, wine and mead. The section starts with the sentence "Wine, beer and traditional sodas all depend on yeast to ferment sugar into alcohol and generate carbonation".
I don't know enough about the history of soda to know if early sodas were alcoholic. Or rather, I am quite sure that there were alcoholic, fermented, carbonated drinks long before what we call "soda" today existed, but I don't know if they were called soda.
Whatever the language problem is, this recipe is definitely intended to produce a low-alcohol beverage, comparable to beer. If you want carbonated syrup, you should buy a carbonating machine. These take a bullet full of CO2 and press it into the drink base you have selected.
As for the too-strong carbonation, this is probably due to the vague term "room temperature". Yeast growth speed depends on temperature. Because it is an exponential growth, even small changes in temperature can lead to vastly different results. If you want to repeat the experiment despite the alcohol production, try better controlling for the temperature. As I don't brew, I can't tell you the temperature for optimal carbonation after two days, you will have to find it out by yourself.
After dumping out a couple of jars of failed not-quite-fermented fennel I wondered, "Could fennel have antimicrobial properties?"
<< facepalm >>
Why, yes. Yes it could:
Granted, these are about the essential oil and not the whole plant. So I can't be sure this is the problem, but it seems very likely.
Maybe a little fennel mixed in with something else won't muck up the fermentation process, whereas a whole jar of fennel can.
And though it's hard to know, I suppose there could be a safety concern. Lacto fermentation protects us through (1) salt, (2) oxygen depletion, and (3) acid production. Based on what I saw with the failed batches, (2) and (3) may have been below normal. If salt-tolerant critters were to survive... that could be bad.
Best Answer
If you feel that your brine, and the resulting kraut is too salty, once your kraut is fermented, you can rinse it before you use it. In fact, there are recipes for sauerkraut (Julia Child's choucroute garni comes to mind), that rinses the kraut several times before braising.