How to find challenges with tags which are now synonymised?
You've probably noticed that you can't just search for a synonym, e.g.
[time] (which is a synonym of date, but still has some questions tagged with it. It is possible to find challenges which are tagged with synonyms of a certain parent, but not the parent itself with the following search query:
Test it here. Note that this turns up only three challenges with the time tag although four exist. I'm assuming the fourth one has both date and time, so it won't be found by this query. I don't know of a good way to find these using the search.
How does synonym renaming work?
When a synonym is created, old challenges won't be retagged automatically. That's why challenges with time, calendar and shortest-code still exist. However, once the synonym is created, any attempt to use the tag will automatically be renamed.
In the case of braces, brackets and parentheses, I added these pre-emptively, so no challenges ever used them.
You can see whether any challenges still have a synonym, you can visit the synonyms page (no privileges required), which shows how often a tag is still use.
Cleaning up synonyms
As for your actual goal of cleaning up all the uses of the old tag, that's honourable, but I don't think it's necessary. The old tag works like the new tag for all intents and purposes. Searching for either brings up all challenges with both tags. There is no separate tag page for the old tag any more. Using the old tag automatically turns into a new tag.
That said, there's also no good reason to keep the old tag around. But for getting rid of it, there's a much better solution than painstakingly trying to find all the challenges that still use it and then retag them one by one: moderators can merge tags. Even quite conveniently straight from the tag synonyms list. Not only is that a lot less effort, it also doesn't create a revision in the affected challenges and doesn't bump all of them to the front page. So if you think some old synonym should be cleaned up, just let a moderator know in chat or post a request here on meta.