[FEATURE] Desktop App: Add the ability to share a private link privately

Preflight Checklist

• [x] I have searched existing requests and this feature hasn't been requested yet
• [x] This is a single feature request (not multiple features)

Problem Statement

I am using the Claude desktop app and I like to link to my claude chats so later on I can use that information to make documentation. I have a lot of chats so it is hard to keep track of them in the App so I was sharing the the conversation and copying that share link, however I discovered that these links were not private.

Now when I create a conversation in the desktop App I have to go the website to copy the URL which does link to my private conversation. This defeat the purpose of using the desktop app.

One further thing, the share chat window implies that when you click Create share link the share link you get is private because of the where the tick is.

<img width="520" height="406" alt="Image" src="https://github.com/user-attachments/assets/c2f791b4-d93f-4b6e-9f54-fa6b10815f2c" />

Proposed Solution

• In the desktop app share window
• Grey out the Create share link button for the option Keep private
• Add a new option Share private link
• The new share link should be available in the format: claude://claude.ai/chat/xxxxxxxx-xxxx-xxxx-xxxx-1318bedf8ace
• On the main chat window
• There should also be a link to take you to the website version of the chat: http://claude.ai/chat/xxxxxxxx-xxxx-xxxx-xxxx-1318bedf8ace

Alternative Solutions

There are no alternatives

Priority

Medium - Would be very helpful

Feature Category

Other

Use Case Example

• Talk with Claude and get lots of information
• I want to male documentation with it so i want to copy the chat link into my notes.txt for later consumption
• I can now use my notes and the chat to make proper documentation

Additional Context

_No response_