A huge issue for SvelteKit (and I presume other frameworks) is that adding a second +page.svelte or +layout.server.ts seems to overwrite the reference to the previous one (at least in the composer UI).
Incidentally, a better way to reference these files based on routes rather than file names would be hugely welcome!
Seconding this bug report. Using Composer with the same file names will cause all kinds of wonky behavior.
For example: I was using Composer on a SvelteKit project and I asked it refactor src/routes/+page.svelte by breaking it up into several pages. It correctly suggested to add pages like src/routes/login/+page.svelte but then failed when it attempted to create the pages or refactor the contents. It kept rewriting over src/routes/+page.svelte over and over.