[FEATURE] Scope Remote Control per session type — reopen: scheduled/Routine sessions still auto-enable it (see #91839)

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

This is the same problem as #77929 (closed not_planned on 2026-09-03), reported again because #91839 (filed the same day) independently confirms the root cause with concrete evidence: every session a scheduled task/Routine spawns gets remoteControlAutoEligible: true set at creation, which is a separate code path from the remoteControlAtStartup ("Connect new sessions to Remote Control") preference — that preference only governs sessions started interactively. So a user can turn "Connect new sessions to Remote Control" off in Settings and still see every Routine-spawned session come up in Remote Control mode immediately, with no persistent way to opt Routines out short of the global disableRemoteControl kill switch, which also blocks Remote Control for sessions the user does want to reach remotely (e.g. checking on a long-running Routine from a phone). The only current workaround is manually toggling Remote Control off per-session after every single run, which doesn't persist to the next scheduled firing.

Proposed Solution

A setting (or a per-Routine toggle in the Routine/scheduled-task editor) that opts scheduled-task-spawned sessions out of Remote Control auto-enable specifically, independent of both remoteControlAtStartup and disableRemoteControl. Given #91839 supplies the mechanism (the remoteControlAutoEligible flag), the fix looks scoped to gating that flag's default based on whether session creation originated from a scheduled task.

Alternative Solutions

Currently using disableRemoteControl: true as the only lever, which forfeits Remote Control for interactive sessions too — not a real workaround, just a full opt-out.

Priority

Medium - Would be very helpful

Feature Category

Configuration and settings

Use Case Example

I run a scheduled task ("Routine") daily on my machine that checks for catalog drift. Each time it fires, the spawned session immediately shows Remote Control connected in the desktop app's session list — even though the global "Connect new sessions to Remote Control" preference in Settings is off. I only want that preference to apply to sessions I start myself in a terminal; I don't want every daily Routine run reachable from claude.ai/code or my phone by default.

Additional Context

Related: #91839 (session-database evidence for remoteControlAutoEligible on scheduled-task sessions), #87777 (reverse-engineered remoteControlAutoEligible / shouldEvaluateRemoteControlPolicy gate).