docs: drop the skin system and src/base_classes from the docs

Deletes docs/SKIN_SYSTEM.md and docs/CREATING_SKINS.md and every link to
them (docs/README.md, README.md, PLUGIN_DEVELOPMENT_GUIDE.md, the /skins
section of REST_API_REFERENCE.md), the skin section of CLAUDE.md and the
term in PRODUCT.md. SPORTS_UNIFICATION.md now says src/base_classes was
removed and shared code lives in src/common, in the Layering section and
the view-model-contract rule. Other docs stop pointing at the removed
package. CHANGELOG records both removals under Unreleased.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

docs/REST_API_REFERENCE.md

@@ -37,7 +37,6 @@ the entry below says so.
 - [Integrations](#integrations)
 - [Plugin-specific endpoints](#plugin-specific-endpoints)
 - [Starlark Apps](#starlark-apps)
-- [Skins](#skins)
 
 > The API blueprint is the `api_v3` package in
 > `web_interface/blueprints/api_v3/` (one module per area: `config.py`,
@@ -2057,17 +2056,6 @@ runs.
 
 ---
 
-## Skins
-
-**GET** `/api/v3/skins`
-
-Installed scoreboard skins (optional `?plugin_id=` filter). Skins are not
-supported by the current scoreboard plugins, so the response carries
-`data.supported: false` and a `data.message`; clients must not offer these
-as selectable. See [SKIN_SYSTEM.md](SKIN_SYSTEM.md).
-
----
-
 ## Error Responses
 
 Errors use one of two shapes. Most endpoints answer: