Right now, the unsyncedlyrics tag is not detected as anything special, which makes it difficult to generalize between different formats, since this appears to be only used for FLAC?

It's a bit hard to tell. Either way, it appears that "lyrics" is generally used for synchronized lyrics, whereas unsyncedlyrics is used for unsynchronized lyrics, and it would be nice for Picard to at least understand the purpose of this tag.

For a bit of extra context, I noticed this issue when trying to use the lrclib plugin to synchronize some lyrics with existing files I have, and maybe update the database to include some of the lyrics tags from files that were not yet uploaded. But, when trying to help implement a replacement, I realised that Picard doesn't actually understand any distinction for this tag, and considering how it also has a synchronized lyrics tag, it's a bit confusing.

Perhaps this tag is nonstandard, since I've also noticed some files I have use "lyrics" as a tag instead, but this appears to be in common use at least.