~anthropic/claude-sonnet-latest → B (65:35)

Side B is a focused, genuine bugfix: it replaces multiple hardcoded staging/production hostnames with a single reusable `get-base-url` util (reducing duplication) and fixes real broken redirects for custom hosts plus corrects the CI deploy trigger to the staging branch. Side A, while large, is mostly a mechanical move of legacy/dead code (`legacy/parser.rs` → `server/src/parser.rs`) with type renames (UIAction→ParserAction) and duplicated test bodies verbatim, which inflates line count without adding much genuinely new, verified logic beyond wiring speculative UI hooks.