Feature Request: Customizable chat prompt to distinguish Q chat windows

### 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

Linux 6.17.7-arch1-2 - Arch Linux

### Expected behaviour

Ability to customize the Q CLI chat prompt (e.g., add a prefix like "[Q]" or change colors) so users can easily distinguish Q chat windows from any shell terminals.

### Actual behaviour

The Q CLI chat prompt is fixed as ">" with no configuration option to customize it

### Steps to reproduce

_No response_

### Environment

```yaml

[q-details]
version = "1.19.6"
hash = "5b649e6f65a0035ad9ee2dbad6c6b7fdb3ddf0c6"
date = "2025-11-13T18:11:44.622413Z (2d ago)"

[system-info]
chip = "Intel(R) Core(TM) i9-14900KF"
total-cores = 24
memory = "62.50 GB"

[system-info.os.linux]
kernel_version = "6.17.7-arch1-2"
id = "arch"
name = "Arch Linux"
pretty_name = "Arch Linux"
build_id = "rolling"

[environment]
cwd = "/home/USER/.config"
cli-path = "/home/USER/.config"
install-method = "unknown"

[env-vars]
DISPLAY = ":1"
EDITOR = "hx"
PATH = "/home/USER/.local/share/mise/installs/node/25.0.0/bin:/home/USER/.local/share/omarchy/bin/:/home/USER/.local/share/../bin:/usr/local/sbin:/usr/local/bin:/usr/bin:/usr/lib/jvm/default/bin:/usr/bin/site_perl:/usr/bin/vendor_perl:/usr/bin/core_perl:/usr/lib/rustup/bin:/home/USER/.local/bin:/home/USER/bin:/usr/local/games"
QT_IM_MODULE = "fcitx"
Q_SET_PARENT_CHECK = "1"
SHELL = "/usr/bin/bash"
TERM = "xterm-256color"
XDG_CURRENT_DESKTOP = "Hyprland"
XDG_SESSION_DESKTOP = "Hyprland"
XDG_SESSION_TYPE = "wayland"
XMODIFIERS = "@im=fcitx"

[chat-settings]

[chat-trusted_tools]
execute_bash=trusted
fs_write=trusted

[chat-failed_request_ids]
none

[chat-context]
current_profile=q_cli_default
profile_context=
AmazonQ.md
AGENTS.md
README.md
.amazonq/rules/**/*.md

files=none
```