docs: fix broken River sync module link in the tutorial

[sanity]

Problem

Err0rz asked on Matrix what happened to River's sync module, because the app-building tutorial links to it:

https://github.com/freenet/river/tree/main/ui/src/sync

That URL 404s. Investigating: the path has never existed in River's git history — git log --all --name-only across every commit shows no ui/src/sync, and at the commit contemporaneous with the doc line (Jan 2026) ui/src/ contained only components/, util/, and a handful of .rs files. So this is a doc error introduced in 7e6dc1f (2026-01-17, "Remove JS/TS UI example, focus on Dioxus/Rust"), not a River refactor that broke a previously-good link.

Nothing is missing from River. The code the tutorial means to point at is at ui/src/components/app/freenet_api/.

Approach

Repoint the link and, while there, name the files a reader actually needs so the link is useful rather than merely non-404. Descriptions verified against River main (419d013):

• connection_manager.rs — the only file calling WebApi::start/WebSocket::new
• freenet_synchronizer.rs — the sync loop / orchestrator
• room_synchronizer.rs — issues ContractRequest::{Get,Put,Subscribe,Update}
• response_handler/ — one module per response kind

It was the only broken github.com/freenet/river link in content/build/ (the other five all resolve).

Testing

hugo builds clean; confirmed the rendered build/manual/tutorial/index.html carries the new href. Both URLs checked over HTTP: old path 404, new path 200.

[AI-assisted - Claude]