Closes #3720

Problem

Agent mode's injected system prompt ([Plan mode — read-only...]) and other controller-injected prefixes leak into the desktop chat UI as visible user messages. This affects:

1. Old sessions (pre-v1.4.0) — no .display.json sidecar exists, so sessionDisplayResolver() falls back to returning raw composed content with PlanModeMarker, <memory-update>, and <background-jobs> blocks intact.
2. Synthetic user messages — planApprovedMessage, stream-recovery messages, readiness-retry messages, and executor-handoff messages are stored as Role: "user" but should never appear in the chat UI. The frontend only filters role === "system" — synthetic messages pass through.

The CLI does NOT have this leak for PlanModeMarker (it already strips it in replaySectionsFor), but it DOES leak <memory-update> and <background-jobs> blocks.

Solution

StripComposePrefixes (new function in internal/control/input.go)

Strips all controller-injected prefixes from a composed user message:

• <memory-update>…</memory-update> blocks (prepended by Compose() when memory is queued)
• <background-jobs>…</background-jobs> blocks (prepended by Compose() for job completions)
• PlanModeMarker + "\n\n" prefix (prepended when plan mode is active)

Used as the fallback in sessionDisplayResolver() when no .display.json sidecar exists — so old sessions display correctly without backfill.

IsSyntheticUserMessage (new function in internal/control/input.go)

Detects known synthetic user messages by exact match (planApprovedMessage) or specific prefixes:

• "Plan approved — plan mode is off"
• "Host final-answer readiness check failed"
• "You are already in the executor phase"
• "The previous assistant response was interrupted while a tool call" / …during streaming" / …before visible"
• "The previous assistant response finished without any visible answer"

Prefixes are specific enough to avoid false positives — a user typing "my response was interrupted by VPN" will NOT be filtered. A sync comment on the syntheticPrefixes var notes it must be kept in sync with the constants in controller.go and agent.go.

Integration points

1. desktop/sessions.go:sessionDisplayResolver() — fallback changed from return content to return control.StripComposePrefixes(content) — fixes old-session leak
2. desktop/app.go:historyMessages() — added if control.IsSyntheticUserMessage(content) { continue } — filters synthetic messages from history
3. internal/cli/chat_tui.go:replaySectionsFor() — changed strings.TrimPrefix(m.Content, PlanModeMarker+"\n\n") to control.StripComposePrefixes(m.Content) — also strips memory/job blocks in CLI session replay

Why this approach

This fix handles both old sessions (via StripComposePrefixes fallback) AND new sessions (via IsSyntheticUserMessage filter), with no session format changes.

Testing

18 new test cases:

• TestStripComposePrefixes — 8 cases: plain message, plan marker stripped, marker alone, memory block, jobs block, memory+marker, empty after strip, memory-only
• TestIsSyntheticUserMessage — 10 cases: plan approved, 3 stream recovery variants, empty final, readiness retry, executor handoff, regular message (false), plan marker (false), interrupted-before-visible variant, and a false-positive test confirming a user typing "my response was interrupted by VPN" is NOT filtered

go vet ./internal/control/... ./internal/cli/...  — clean
go test ./internal/control/... ./internal/cli/...  — pass
gofmt — clean (CRLF working-copy warnings only, committed content uses LF)