service: make subprocess PATH deterministic across reconnect election

Summary

The V2 managed background service inherits the environment of whichever reconnecting client wins service election. When several clients reconnect after a restart, crash, or version replacement, they race to spawn detached contenders with potentially different PATH values.

The winning environment becomes the process-global environment used by shell calls. As a result, the same command can work before a service replacement and fail afterward with command not found (observed with curl).

Reproduction

A bounded harness exercised the current Service.ensure path with two simultaneous reconnecting clients:

1. Client A had a PATH containing a fixture curl executable.
2. Client B had a PATH without curl.
3. Both called Service.ensure concurrently after the registration disappeared.
4. The elected service ran /bin/sh -c curl using its inherited environment.
5. The election was repeated 20 times.

Result:

{"found":10,"missing":10}

The command outcome depended only on which client's contender won election.

Cause

• packages/client/src/effect/service.ts spawns each contender with inherited environment via spawn(command, args, { detached: true, stdio: "ignore" }).
• A restart or service loss causes every attached client reconnect loop to call Service.ensure, so contenders may originate from different terminal, IDE, or launcher environments.
• packages/core/src/shell.ts builds every shell environment from the elected server's process.env.
• Repository search found no production path that deletes, replaces, or mutates PATH; this is environment replacement across server processes, not mutation within one server.

This is adjacent to the reconnect herd documented in #36285, but the user-visible failure here is nondeterministic process environment rather than contender resource overhead.

Expected behavior

Shell command resolution should remain deterministic across managed-service replacement and should not depend on which attached client wins a reconnect race.

Design options

1. Canonical service environment: derive the service environment from the user's login shell on startup, independent of the spawning contender. Desktop already has a bounded login-shell environment probe that may be reusable after extraction.
2. Persist a canonical local environment: choose and retain one non-secret environment contract across service replacements. This needs careful treatment of changing toolchains and secret values.
3. Explicit client/session environment: pass the relevant execution environment through an owned client, session, or location boundary rather than relying on server-global process.env. This is more precise but requires conflict semantics for multiple clients.

Questions

• Which boundary should own local command environment in the shared-service architecture?
• Should activated environments such as mise, direnv, Nix, or virtualenv follow the client/session, or should the service always use a canonical login-shell environment?
• What environment data is safe to persist or send over the local API?
• Should shell, PTY, MCP, LSP, formatter, and other subprocess producers share one environment policy?

Source discussion: https://slack.com/archives/C0BE69AHCQP/p1785009702750149

Requested by: @rekram1-node (Aiden Cline via Slack)