Rebases @ashishexee's #3738 onto current main-v2. The only conflict was a trivial import merge in desktop/sessions.go (main-v2 added internal/agent, the PR added internal/control) — both are used, so both imports are kept.

Strips controller-injected prefixes ([Plan mode — read-only…] marker, <memory-update>, <background-jobs> blocks) and synthetic Role: "user" messages from the chat display, so agent-mode internals no longer leak into the desktop/TUI transcript.

Verification

• control.StripComposePrefixes covered by TestStripComposePrefixes (8 sub-cases: plan marker, memory-update, background-jobs, combined, empty-after-strip) — all pass
• Root module go build ./..., internal/control and internal/cli tests, and the desktop module go build ./... all green after the merge

Closes #3738

Credit: @ashishexee