Session memory should persist when forking or sending to new chat

[digitarald]

When using "Send to New Chat" or forking a conversation, the current session memory is not carried over to the new chat session. This means that any session-specific context, state, or accumulated knowledge from the current conversation is lost, requiring users to rebuild that context manually.

Expected Behavior:

• Session memory should be preserved when creating a new chat via "Send to New Chat" (Ctrl+Shift+Enter)
• Session memory should be maintained when /fork forking conversations
• Context accumulated during the conversation should be available in the new chat

Current Behavior:

• New chat sessions start fresh without any session memory
• Users must re-establish context and provide information again
• This interrupts workflow and reduces productivity

cc @pierceboggan as /fork owner