[FEATURE] Add persistent total cost tracking across compactions

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

When a conversation gets compacted (either manually via /compact or automatically when context limits are reached), the /cost counter resets to $0. This makes it impossible to know the true total cost of a session.

Use case: When working on a feature or project within a single session, the conversation often gets compacted multiple times. I'd like to know the total cost of the entire session, not just the cost since the last compaction.

Current behavior:

• /cost shows usage only since the last compaction
• After compaction, the counter resets to $0
• No way to retrieve the cumulative cost

Expected behavior:

• /cost should show both the current segment cost AND the cumulative session total

Example output could include a line like Total session cost: $X.XX alongside the current segment breakdown

Workaround: Manually noting down /cost before each compaction and adding them up, which is error-prone and easy to forget.

Proposed Solution

Persist a running total — Before each compaction, snapshot the current cost and add it to a running total stored in session metadata (outside the conversation context that gets compacted).

Display both values in /cost — Show "Current segment" and "Total session" as separate lines.

Optional: Session summary file — On session end or on demand, write a cost summary to a local file (e.g., ~/.claude/sessions/<id>/cost.json) so users can reference it later for project budgeting.

Optional: /cost --all — A flag to list cost breakdown per segment (e.g., Segment 1: $12.52, Segment 2: $2.34, Segment 3: $0.38).

Alternative Solutions

_No response_

Priority

Critical - Blocking my work

Feature Category

CLI commands and flags

Use Case Example

I'm working on a feature that requires multiple rounds of code exploration, implementation, debugging, and testing — all within a single session. The conversation gets compacted 3-4 times as context fills up. At the end, I want to report the total AI-assisted development cost for this feature to my team/manager, but /cost only shows the last segment ($0.38) instead of the real total (~$15+). I have no way to recover the earlier costs.

Additional Context

This is especially important for enterprise/team usage where developers need to track and justify AI tooling costs per feature or sprint

Users on usage-based billing plans need visibility into actual spend to stay within budgets

Long-running sessions (1-3 hours) for complex features almost always trigger multiple compactions, making this a frequent pain point

The data is already being calculated per segment — it just needs to be accumulated rather than discarded

This would also help users make informed decisions about when to start a new session vs. continue an existing one