docs: improve user-server docs readability and references

Co-Authored-By: Claude Code <[email protected]>

docs/hosting.md

@@ -3,14 +3,14 @@
 `horizon-server` hosts a Minecraft Java Edition 26.3 server with Horizon's own game as the engine: one native
 program, no Java, one settings file, a command line, and a web panel. Vanilla 26.3 clients and Horizon clients
 can join it. This page covers what works on `main` today and says plainly what doesn't yet. The design and the
-plan are in [docs/server.md](https://github.com/horizon-rust/horizon/blob/main/docs/server.md).
+plan are in [server.md](server.md).
 
 ## Before you start
 
 - **Online mode checks accounts** (release v2026.10.17.07 and newer). With `online_mode = true`, the
   default, every player joins with their own account, as on a vanilla server: vanilla players signed in with
   the official Minecraft launcher, Horizon players with the Microsoft account they signed in with in Horizon's
-  launcher ([docs/microsoft-account.md](https://github.com/horizon-rust/horizon/blob/main/docs/microsoft-account.md)).
+  launcher ([microsoft-account.md](microsoft-account.md)).
 - **Names you add are accounts** (release v2026.10.17.14 and newer). `init --player`, `horizon-server
   whitelist add` and `op`, and the console's `whitelist add`, `op` and `ban` look a name up the way vanilla
   does: players already seen (kept in `usercache.json`), then Mojang's profile service. In online mode a name

docs/owners.md

@@ -75,7 +75,7 @@ These belong to `horizon-server`, not to the game:
 
 ## Planned: limiting a server to Horizon clients
 
-The design (`docs/design.md`, section 6 of horizon-rust/horizon-server) adds one more setting. It is not in
+The design ([server-next.md](server-next.md#6-who-can-join), section 6) adds one more setting. It is not in
 `server.toml` yet.
 
 ```toml

docs/server.md

@@ -7,8 +7,7 @@ should beat vanilla, Paper and Fabric + Lithium on TPS/MSPT, RAM, CPU, chunk gen
 Gameplay stays vanilla: there are no Paper-style rule changes unless the owner turns one on.
 
 This page covers what the server does today (measured), the design of `horizon-server`, and what ships for the
-first working version (2026-10-23). The owner's guide is docs/hosting.md, also at
-https://playhorizon.dev/server.
+first working version (2026-10-23). The owner's guide is [docs/hosting.md](hosting.md).
 
 ## 1. Today