I can imagine it is slow, beings as you are calling system.tag.browse() which is already a slow-ish function for every tag at the root path.
Instead, you should use the filter to filter for only the tags that you need and do so recursively, then you can loop through that list adding your custom property where needed building a list of tag paths, then read all of the tags at once.
Also, it looks like you are adding `"/Overview" to the full path of a tag, however, the full path includes the tag name, so unless the "tag" is a folder, then that path would be invalid.
I guess I don't understand your tag structure, so I can't really provide useful code, but I would expect you to build a list of all tags to be read, then split that into two lists as you can count on the order, and then build your instances list from that.
Here is another thread that shows something similar to what I would expect, note not all of this applies, you can pretty much ignore the DB stuff for your purposes.