Inline autocomplete does not render inside herdr panes (but works fine outside)

### Checks

- [x] I have searched [github.com/aws/amazon-q-developer-cli/issues](https://github.com/aws/amazon-q-developer-cli/issues?q=) and there are no duplicates of my issue
- [x] I have run `q doctor` in the affected terminal session
- [x] I have run `q restart` and replicated the issue again

### Operating system

macOS 26.5.2 (25F84)

### Expected behaviour

The autocomplete should be visible

### Actual behaviour

No autocomplete dropdown is visible

### Steps to reproduce

1. Start a herdr session (`herdr` or `herdr --session `), open a pane.
2. Inside that pane, start typing a shell command.
3. Expected: inline suggestion/ghost text appears (as it does in a plain terminal tab).
4. Actual: no suggestion ever renders.

### Environment

```yaml

[q-details]
version = "2.14.1"
hash = "a190cd43fc06af5fe93fcd74ceadc5509009cd3f"
date = "2026-07-23T04:45:29.789871Z (1d ago)"
variant = "full"

[system-info]
os = "macOS 26.5.2 (25F84)"
chip = "Apple M1 Pro"
total-cores = 10
memory = "16.00 GB"

[environment]
cwd = "/Users/USER/Dev/taman-biner/ngibur"
cli-path = "/Users/USER/Dev/taman-biner/ngibur"
os = "Mac"
shell-path = "/bin/zsh"
shell-version = "5.9"
terminal = "Ghostty"
install-method = "unknown"

[env-vars]
PATH = "/Users/USER/google-cloud-sdk/bin:/Users/USER/.rbenv/shims:/Users/USER/.local/bin:/Users/USER/.antigravity-ide/antigravity-ide/bin:/Users/USER/.antigravity/antigravity/bin:/Users/USER/Library/pnpm/bin:/Users/USER/Library/Android/sdk/platform-tools:/Users/USER/.deno/bin:/Users/USER/.yarn/bin:/Users/USER/.config/yarn/global/node_modules/.bin:/Users/USER/flutter/bin:/Users/USER/.bun/bin:/usr/local/sbin:/Users/USER/.local/bin:/opt/snowflake/snowcd:/Library/Frameworks/Python.framework/Versions/3.12/bin:/opt/homebrew/bin:/opt/homebrew/sbin:/Users/USER/.local/bin:/usr/local/bin:/System/Cryptexes/App/usr/bin:/usr/bin:/bin:/usr/sbin:/sbin:/var/run/com.apple.security.cryptexd/codex.system/bootstrap/usr/local/bin:/var/run/com.apple.security.cryptexd/codex.system/bootstrap/usr/bin:/var/run/com.apple.security.cryptexd/codex.system/bootstrap/usr/appleinternal/bin:/pkg/env/global/bin:/Library/Apple/usr/bin:/usr/local/go/bin:/opt/podman/bin:/Users/USER/google-cloud-sdk/bin:/Users/USER/.rbenv/shims:/Users/USER/.antigravity-ide/antigravity-ide/bin:/Users/USER/.antigravity/antigravity/bin:/Users/USER/Library/pnpm/bin:/Users/USER/Library/Android/sdk/platform-tools:/Users/USER/.deno/bin:/Users/USER/.yarn/bin:/Users/USER/.config/yarn/global/node_modules/.bin:/Users/USER/flutter/bin:/Users/USER/.bun/bin:/usr/local/sbin:/opt/snowflake/snowcd:/Library/Frameworks/Python.framework/Versions/3.12/bin:/Applications/Ghostty.app/Contents/MacOS:/Applications/Visual Studio Code.app/Contents/Resources/app/bin:/Users/USER/go/bin:/Users/USER/.spicetify:/Applications/Visual Studio Code.app/Contents/Resources/app/bin:/Users/USER/go/bin:/Users/USER/.spicetify"
QTERM_SESSION_ID = "8cd3ed72ba9d43ebb4bb28da3a733c95"
Q_SET_PARENT_CHECK = "1"
Q_TERM = "2.14.1"
SHELL = "/bin/zsh"
TERM = "xterm-256color"
__CFBundleIdentifier = "com.mitchellh.ghostty"
```

Reproduce the issue in a herdr pane and compare it with a plain terminal tab, using the reported macOS, Ghostty, zsh, and version 2.14.1 environment details as context. Trace the autocomplete suggestion and rendering paths for pane sessions; done means inline ghost text or the autocomplete dropdown appears inside herdr panes as it does outside them.

Written by the indexing model from the issue text.