Seems pretty convenient for avoiding opening the kanji pages in new tabs. 
I’m assuming it only works for readings taught during kanji lessons? Or does it also help for items like 見当たる?
For 誇大 I get an error. In the line
&& frontRendakuTransforms[wordChar].includes(possibleChar)) {
wordChar is “だ” which is not in frontRendakuTransforms.
I have also noticed that sometimes your info is not added when I’m opening the item info – in these cases I have to close and reopen it. Maybe there is a race condition? I only took a glance at your code and noticed a setTimeout(handleNewItem, 200) – but maybe that’s unrelated to the problem.
It might be nice if your info is also added after a meaning question when the user completely expands the item info to also view the reading info.
More generally, I think it would be useful if your info would also be available during lessons, extra studies, and on the item pages.
And now some shameless self promotion 
Since writing code for injecting additional item info into WK can become annoying, I have written the library script “WK Item Info Injector”. You could use it to get notified when a new reading info section was created[1] and insert your DOM elements yourself, or you could let WK Item Info Injector handle the insertion[2].