docs(llm-wiki): add Obsidian Headless setup for servers (#5660)

Adds obsidian-headless (npm) setup guide to the Obsidian Integration
section — Node 22+, ob login, sync-create-remote, sync-setup, systemd
service for continuous background sync. Covers the full headless
workflow for agents running on servers syncing to Obsidian desktop on
other devices.

skills/research/llm-wiki/SKILL.md

@@ -380,6 +380,62 @@ For best results:
 If using the Obsidian skill alongside this one, set `OBSIDIAN_VAULT_PATH` to the
 same directory as the wiki path.
 
+### Obsidian Headless (servers and headless machines)
+
+On machines without a display, use `obsidian-headless` instead of the desktop app.
+It syncs vaults via Obsidian Sync without a GUI — perfect for agents running on
+servers that write to the wiki while Obsidian desktop reads it on another device.
+
+**Setup:**
+```bash
+# Requires Node.js 22+
+npm install -g obsidian-headless
+
+# Login (requires Obsidian account with Sync subscription)
+ob login --email <email> --password '<password>'
+
+# Create a remote vault for the wiki
+ob sync-create-remote --name "LLM Wiki"
+
+# Connect the wiki directory to the vault
+cd ~/wiki
+ob sync-setup --vault "<vault-id>"
+
+# Initial sync
+ob sync
+
+# Continuous sync (foreground — use systemd for background)
+ob sync --continuous
+```
+
+**Continuous background sync via systemd:**
+```ini
+# ~/.config/systemd/user/obsidian-wiki-sync.service
+[Unit]
+Description=Obsidian LLM Wiki Sync
+After=network-online.target
+Wants=network-online.target
+
+[Service]
+ExecStart=/path/to/ob sync --continuous
+WorkingDirectory=/home/user/wiki
+Restart=on-failure
+RestartSec=10
+
+[Install]
+WantedBy=default.target
+```
+
+```bash
+systemctl --user daemon-reload
+systemctl --user enable --now obsidian-wiki-sync
+# Enable linger so sync survives logout:
+sudo loginctl enable-linger $USER
+```
+
+This lets the agent write to `~/wiki` on a server while you browse the same
+vault in Obsidian on your laptop/phone — changes appear within seconds.
+
 ## Pitfalls
 
 - **Never modify files in `raw/`** — sources are immutable. Corrections go in wiki pages.