feat(enforcer): raise manual pick cap from 2 to 3 concurrent games

Config.max_manual_picks is the single source of truth for how many
games may be locked in at once; enforcement, CLI, and MCP tooling all
already read it dynamically. Updates docs referencing the old default.

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

docs/explanations/2026-07-19-explanation-manual-pick-grace-and-multi-pick.html

@@ -113,7 +113,7 @@
 <body>
 
 <h1>Manual picks: a way out, and a second slot</h1>
-<p class="sub">Two changes to the Steam Backlog Enforcer — a 4-day window to undo a manual pick, and support for two locked-in games at once. Commits <code>eb1472a</code> and <code>05e070c</code>, 19 July 2026.</p>
+<p class="sub">Two changes to the Steam Backlog Enforcer — a 4-day window to undo a manual pick, and support for up to three locked-in games at once. Commits <code>eb1472a</code> and <code>05e070c</code>, 19 July 2026.</p>
 
 <nav class="toc">
   <strong>Contents</strong>
@@ -227,9 +227,9 @@ abandon that one. Each new pick stamps a fresh <code>started_at</code>, so the g
 forever and the enforcer enforces nothing.</p>
 
 <p>The chosen answer was not to forbid re-picking, but to make a second concurrent pick a
-first-class, <em>capped</em> feature. If you may legitimately have two games locked in, correcting
+first-class, <em>capped</em> feature. If you may legitimately have several games locked in, correcting
 a pick no longer requires a pick→abandon→pick cycle, and the cap is what bounds the whole thing.
-<code>Config.max_manual_picks</code> defaults to 2.</p>
+<code>Config.max_manual_picks</code> defaults to 3.</p>
 
 <p>That turns the enforcer's central question from "which game?" into "which <em>set</em> of
 games?" — and that is the real substance of the diff:</p>

steam_backlog_enforcer/config.py

@@ -60,7 +60,7 @@ class Config:
     kill_unauthorized_games: bool = True
     uninstall_other_games: bool = True
     desktop_notifications: bool = True
-    max_manual_picks: int = 2
+    max_manual_picks: int = 3
     """How many games may be manually locked in at once.
 
     All active picks stay installed and visible; the enforcer treats them as

steam_backlog_enforcer/docs/pick_game_manually_design.md

@@ -39,11 +39,11 @@ full 2 weeks. There is now a short mistake-correction window:
 The lock-active message advertises `abandon-pick` only while the window is
 still open, and the `pick-manual` warning mentions it up front.
 
-## Two concurrent manual picks (added 2026-07-19)
+## Concurrent manual picks (added 2026-07-19)
 
-`Config.max_manual_picks` (default 2) is how many games may be locked in at
-once. Both stay installed, visible and un-killed; the lock releases only when
-every pick is finished or past its own 14-day deadline.
+`Config.max_manual_picks` (default 3) is how many games may be locked in at
+once. All active picks stay installed, visible and un-killed; the lock
+releases only when every pick is finished or past its own 14-day deadline.
 
 - `State.manual_picks` is the list of `{app_id, game_name, started_at}`
   entries. The old single-slot `manual_pick_*` fields are still read on load,
@@ -52,15 +52,15 @@ every pick is finished or past its own 14-day deadline.
   source of truth for "may exist". `uninstall_other_games`,
   `hide_other_games`, `enforce_allowed_game` and `_guard_installed_games` all
   take that set instead of one app id.
-- `pick-manual` is in `_MANUAL_LOCK_EXEMPT_COMMANDS` so a second game can be
-  added while the first holds the lock; the cap is what limits it. Its
+- `pick-manual` is in `_MANUAL_LOCK_EXEMPT_COMMANDS` so another game can be
+  added while earlier picks hold the lock; the cap is what limits it. Its
   post-pick cascade operates on the whole allowed set, so adding a pick never
   tears down an earlier one.
 - `abandon-pick <app_id>` drops only that pick; a survivor inherits the
   assignment and keeps the lock.
 - `cmd_done` still finishes `current_app_id` and auto-picks a replacement, so
-  two games stay queued. A finished pick leaves the active set automatically
-  via `finished_app_ids` — no pruning needed.
+  the remaining picks stay queued. A finished pick leaves the active set
+  automatically via `finished_app_ids` — no pruning needed.
 
 **Deployment note:** the enforce daemon holds the allowed set in code, so
 `sudo systemctl restart steam-backlog-enforcer` is required after upgrading.