Enhance CopyPage layout and functionality + Copilot link

[clicktodev]

Why:

Closes: #4779

What's being changed (if available, include any code snippets, screenshots, or gifs):

Adjust the layout of the CopyPage component within ClientWrapper for better alignment.
Add copilot link.
Introduce a new CopyCheckIcon to provide visual feedback when content is copied.
Use link component directly for better a11y.
Add open and close animations
Change copy icon to markdown icon in list item

Screen.Recording.2025-09-11.at.11.19.24.AM.mp4

Check off the following:

• I have reviewed my changes in staging, available via the View
  deployment link in this PR's timeline (this link will be available after
  opening the PR).

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[clicktodev]

@dimaMachina

[dimaMachina]

I would prefer keep Copied text after clicking (we need fixed with for button), also now there is a gap of unused space

[clicktodev]

it's usually best to keep the button label the same and just change the icon to indicate the action state (loading, success).
also changing the button label causes content shift as you can see in the linked issue.

the open ai docs don't change the text as well which helps avoid button resize and potential content shift.

same with shadcn docs

the openai docs implement the button on the same line as the page title with flex wrap which works pretty nicely.

[clicktodev]

I personally don't mind the extra space, we can use it as a command bar for more tools in the future.
I also think it makes sense to separate it since it's not part of the md content.

or we can put the copy button on the right above the toc component when it's rendered.
when the toc component isn't rendered, then we fallback to the current render position on top of the page title.