I spent about 30-minutes playing around with importing songs after reading your post and the manual carefully.
I'm still finding this a bit counterintuitive. Currently, I do all my lyric editing externally. I could use the built-in editor eventually for fixes, but I'm not doing that yet. The other day, for example, I removed the trailing silence from all my tracks using GoldWave which does batch processing. Easy. Then I wanted to bring the songs back into ST3. Easy too: Edit > Select All > Delete All > + > Import From Local & Cloud Files > Select All (or just 30 at a time to avoid errors) > Open. Done. Playlists obviously destroyed. But the point is that was mostly effortless. The same thing when I make changes to multiple lyric files, which are separate to the MP3s on my PC (before I run a program to combine them.) Why would I edit so many lyric files: Well I use lyrics for things other than just lyrics. One of the most valuable things I have in there is details about the song that I might talk about before I start the song. That includes some facts, who wrote it, sung it, and what year, and some other nonsense to enhance my audience interaction. So sometimes I make changes to many lyric files when I feel like adding more details, etc.
What I find counterintuitive is that if I import these songs without first deleting them, importing makes no changes to any of the existing files, even if I pull down to refresh. I'm expecting there to be a popup asking "Do you want to replace your songs?" or similar. So I tried the suggestion of replacing the MP3s directly in the Files App. This is somewhat slower, but not a major problem. Now I have to think which songs I might have changed lyrics on and go through them one-by-one by opening the lyrics editor and resetting lyrics. That's a bit more work. Then, I use my iPhone as a backup to my iPad so I have to do all this again on my iPhone. It's okay to do this one time, but updating backtracks is a bit of an obsession which I regularly do to improve my performance.
Would it be possible to add some settings option titled "Importing replaces existing lyrics" and "Importing replaces existing files?"
If not, is there already a way to export just the playlists so I can import the songs the easy way and just reload/relink the playlists after that? Using the Files App on iOS is often problematic, and maybe a bit confusing for other people too.