The dialog in question was rendering a form, and by removing one element at a time I was able to determine that one specific text-entry field was causing the issue.
The problem stemmed from the LastPass browser extension trying to provide the option of auto-fill for that field. If I shortened the width of the field, it no longer caused the error. If I disabled the LP auto-fill icon from appearing, it also solved the issue. I chose the latter, since this was not something that LP could really auto-fill anyway.
I don’t know why this only triggered when I upgraded from v5 to v6 of react-router-dom. Our staging and production instances that have not yet received the upgraded code work fine with the LP icon present in the field. Nonetheless, the issue is fixed for me.