[BUG] MCP tool calls stop executing when switching from Home/chat to Code tab

Summary

When a conversation in the Home/chat view is actively running an MCP tool call, switching to the Code tab causes that in-progress MCP work to stop instead of continuing in the background. The user has to stay on the chat tab for the call to complete, defeating the purpose of being able to quickly check something else while work is running.

Current behavior

Start an MCP tool call in a Home-tab conversation, then switch to the Code tab to check something else. The MCP call in the original conversation ceases to make progress while the Code tab is active, rather than continuing to run in the background and simply updating the conversation whenever the user returns to it.

Motivation

This directly undercuts the value of having Home and Code as separate views in the same app — if switching between them pauses whatever's running, the two views can't actually be used concurrently, only serially. Combined with the lack of multi-window support (#30154), this means there's currently no way to have an MCP-driven conversation keep working while doing anything else in the app at the same time.

Proposed behavior

MCP tool execution (and agent work generally) in a Home-tab conversation should continue running in the background regardless of which tab is currently focused, the same way a background subagent or scheduled Routine keeps running unattended. Switching tabs should never pause in-flight work; it should just change what's currently displayed.

Why it matters

Without this, "quickly check something in Code while an MCP call runs" isn't actually possible — the user has to choose between watching progress and doing anything else in the app, one at a time.

Related issues (adjacent, not duplicates)

• #30154 FEATURE: Multi-window support in Claude Code Desktop — adjacent; either multi-window or non-pausing background tabs would independently solve the "I want to do two things at once" problem, though they're different fixes.

Notes

• Reviewed for duplicates before filing (searched "MCP tool call pauses switching Code tab Home", "conversation pauses navigating away background execution", "agent stops running tab switch desktop foreground", "inactive tab suspend session throttle") — nothing found describing tab-switch pausing MCP/tool execution specifically, as of 2026-07-19.