[FEATURE] Method to Cross-link specific Claude Code sessions with claude.ai chat sessions that need content reference

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

Summary
There's currently no way to reference or pull content from a Claude Code session into a claude.ai chat session (or vice versa). When work starts in Claude Code (terminal diagnostics, infra config, file edits) and later needs to be discussed, summarized, or handed off in a claude.ai chat — or when a chat-side decision needs to inform an active Code session — the only options are manual copy-paste (token costly), requesting Claude generate a session summary (lossy), or losing context entirely.

Problem

• Claude Code sessions are stored locally (~/.claude/projects/) and tied to project path + machine; they aren't visible or searchable from claude.ai.
• claude.ai's conversation_search / memory tools only index claude.ai chat history, not Code sessions.
• Users working across both surfaces (e.g., infra work in Code, planning/tracking in chat) have to manually restate Code session context in chat, or export/paste raw transcripts.
• This gets worse across multiple machines/accounts, where a Code session may not even be locally accessible to the person now working in chat.

Proposed Solution

Requested feature
A lightweight link/reference mechanism so a claude.ai chat can pull relevant context from a named Code session (or vice versa) — e.g.:

• A way to tag or name a Code session so it can be referenced by ID/name from a chat
• A chat-side tool (similar to conversation_search) that can search/retrieve Code session transcripts or summaries, scoped to sessions the user has access to
• At minimum, a supported "handoff" export format from Code that a chat session could ingest as structured context rather than a flat text transcript
• If a handoff export of each session could be uploaded periodically to account storage, reference by name or code-session id (which could be searched as a lookup) could happen from any surface the user needs.

Ideally, this process should work while using Chat in Claude Desktop to reference local Claude Code (in Claude Desktop) sessions. Then the further reach of the feature can be added incrementally. For my specific case, I am most likely to need this in the Windows version of Claude Desktop. But doing this properly could allow for cross-reference in a mobile app chat about a Code work session that was done in terminal days ago.

Alternative Solutions

My current prompt for referencing Chat sessions in other contexts is
Can you summarize this conversation in a way that's useful for a different agent session to pick it up and incorporate it into work it's currently doing?
That works well for carrying a chat summary to other places, but not well for varieties of code and repo layouts (that may or may not have formal decision structures) going in the direction of chat sessions.

Priority

High - Significant impact on productivity

Feature Category

Other

Use Case Example

Solo IT/infra admin runs long Claude Code sessions doing hands-on deployment work (AWS/infra config, diagnostics), then switches to claude.ai chat for planning, prioritization, and non-technical drafting. Needing to reference "what did the Code session already do/decide" from chat currently requires manual re-summarization.

Additional Context

_No response_