chore(design-system): centralise MCP client assets (#43730)

## What kind of change does this PR introduce?

Chore

## What is the current behavior?

- We use the MCP client connect dialog in two places: Studio and Docs
- We duplicate image assets for each client in each of those two places

## What is the new behavior?

- Centralised assets
- Consolidation and simplification as a result of it all being a single
source-of-truth now

## To test

- [ ] Everything works as it did before across both Studio and
[Docs](https://supabase.com/docs/guides/getting-started/mcp)
- [ ] All MCP client images load as expected

Author: dnywh

apps/docs/features/ui/McpConfigPanel.tsx

@@ -322,7 +322,6 @@ export function McpConfigPanel() {
             : 'Project selection is only available for the hosted platform.'}
         </p>
         <McpConfigPanelBase
-          basePath="/docs"
           className="mt-6"
           projectRef={project?.ref}
           theme={resolvedTheme as 'light' | 'dark'}

apps/docs/public/img/mcp-clients/antigravity-icon.svg

@@ -1,6 +1,5 @@
 import { IS_PLATFORM, useParams } from 'common'
 import Panel from 'components/ui/Panel'
-import { BASE_PATH } from 'lib/constants'
 import { useTrack } from 'lib/telemetry/track'
 import { useTheme } from 'next-themes'
 import { useMemo, useState } from 'react'
@@ -64,7 +63,6 @@ const McpTabContentInnerLoaded = ({
 
   return (
     <McpConfigPanel
-      basePath={BASE_PATH}
       projectRef={projectRef}
       theme={resolvedTheme as 'light' | 'dark'}
       isPlatform={IS_PLATFORM}

apps/studio/components/interfaces/Connect/McpTabContent.tsx

@@ -1,5 +1,5 @@
 import { useParams } from 'common'
-import { BASE_PATH, IS_PLATFORM } from 'lib/constants'
+import { IS_PLATFORM } from 'lib/constants'
 import { useTrack } from 'lib/telemetry/track'
 import { useMemo } from 'react'
 import {
@@ -79,7 +79,6 @@ function McpCursorContentInner({
     <McpConfigurationDisplay
       className="space-y-4"
       theme="dark"
-      basePath={BASE_PATH}
       selectedClient={selectedClient}
       clientConfig={clientConfig}
       onCopyCallback={handleCopy}