feat(web): integrate custom providers into the provider credentials section

- Merge the separate custom-providers section into the unified provider
  grid; "Custom" in the add-provider picker now acts as an add-new action
  (trailing + mark) and opens the dedicated modal, supporting multiple
  OpenAI-compatible endpoints
- Simplify the custom provider modal: drop the default-model field, add
  an inline delete button, align colors with the theme
- Keep the legacy single "custom" card visible (models page, chat
  dropdown and legacy config page) while custom_api_key/custom_api_base
  is still in use, so existing single-provider setups don't disappear
- Unify user-facing wording from "vendor" to "provider" in UI and docs
- Restructure custom provider docs (zh/en/ja) around Web console and
  config file usage

docs/models/openai.mdx

@@ -25,7 +25,7 @@ OpenAI offers the most complete coverage and can simultaneously serve text chat,
 | `model` | Same as OpenAI's [model parameter](https://platform.openai.com/docs/models); supports `gpt-5.5`, `gpt-5.4`, `gpt-5.4-mini`, `gpt-5.4-nano`, the `gpt-5` series, `gpt-4.1`, the o-series, etc. Agent mode defaults to `gpt-5.5`; use `gpt-5.4` for better cost-efficiency |
 | `open_ai_api_key` | Create one on the [OpenAI Platform](https://platform.openai.com/api-keys) |
 | `open_ai_api_base` | Optional; change it to access a third-party proxy |
-| `bot_type` | Not required when using OpenAI's official models; set to `openai` when accessing other vendors via the compatible protocol |
+| `bot_type` | Not required when using OpenAI's official models; set to `openai` when accessing other providers via the compatible protocol |
 
 ## Image Understanding