[Feature Request] Sessions as first-class, org-scoped, shareable artifacts with cross-developer handoff support

Bug Description
Feature request: sessions as first-class, shareable artifacts (cross-developer handoff)

Use case: on-call engineer gets a Sentry alert, does RCA in a Claude Code session, then needs to hand the live thread to the owning engineer to write the fix + tests and merge. Today this isn't possible —
/remote-control keeps the session local, --remote + --teleport are tied to the originating account, the JSONL file is machine-local and keyed to the cwd path, and session sharing is view-only.

The workaround is async baton-pass via a branch + RCA doc, which throws away the most valuable part of the thread: the reasoning, the dead ends, the "why not X" answers that never make it into a PR description.

Bigger picture: I think threads are going to replace PRs and docs as the primary engineering artifact for a lot of work — they're executable, they answer follow-ups, they preserve reasoning under uncertainty. But
for that to happen, a session needs the properties a PR already has: shareable, forkable, permissioned, durable across accounts, org-scoped. Right now it has none of those. It's a file on one laptop.

The missing primitive isn't "add a share button on /remote-control." It's "a session is a first-class object in the org." Concretely:

• Org-scoped session storage (not ~/.claude/projects/)
• A session has an owner, ACLs, and a URL
• Another org member can continue it (not just view), forking if needed
• Works across --remote and local sessions
• Survives model/tool-environment changes well enough to replay

The handoff flow falls out of that naturally, and so do a bunch of other workflows (pair debugging, review-by-continuation, thread-as-runbook).

Environment Info

• Platform: darwin
• Terminal: ghostty
• Version: 2.1.101
• Feedback ID: dc64adcb-a360-41b4-8b06-706aaa95c8f2

Errors

[{"error":"Error: NON-FATAL: Lock acquisition failed for /Users/rahulbalakavi/.local/share/claude/versions/2.1.101 (expected in multi-process scenarios)\n    at Oc_ (/$bunfs/root/src/entrypoints/cli.js:2836:2153)\n    at Ve6 (/$bunfs/root/src/entrypoints/cli.js:2836:1233)\n    at processTicksAndRejections (native:7:39)","timestamp":"2026-04-11T10:20:54.580Z"}]