Split backend into internal packages by responsibility

All Go files lived flat in backend/ as one package main. Move store,
latest-chapter polling, sessions, HTTP middleware, the JSON API, the
userscript handler, and the web UI (with its templates/static assets)
into backend/internal/{store,latest,session,httpmw,api,userscript,web},
each with an exported API. main.go becomes the composition root wiring
them into newRouter; root-level tests cover the assembled router while
package-local tests cover unit behavior. Update Dockerfile/.dockerignore
for the new internal/ tree and CLAUDE.md to describe the layout.

Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>

backend/.dockerignore

@@ -1,10 +1,8 @@
-# Only go source + module files, plus the go:embed'd templates/static
-# directories, are needed in the build context.
+# Only go source + module files, plus internal/ (which carries the
+# go:embed'd templates/static directories), are needed in the build context.
 *
 !go.mod
 !go.sum
 !*.go
-!templates/
-!templates/**
-!static/
-!static/**
+!internal/
+!internal/**