ZSH Terminal Messed Up By Q Cli Terminal Integration

### 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 15.4.1 (24E263)

### Expected behaviour

I expected Q CLI to work correctly with my ZSH terminal and not interfere with VIM.

### Actual behaviour

Installing Q CLI made my ZSH terminal unusable. I use a multi-line terminal prompt and the Q CLI integration made the terminal usable buffer smaller (about half the horizontal space) and when commands wrap around it results in text disappearing. This issue persists even in VIM. Entering VIM results in a buffer that is only approximately a quarter of the full window.

- text wrap-around happens incorrectly (before reaching the end of the prompt horizontal window size)
- when text wraps around in the prompt, the text becomes unreadable
- when attempting to delete characters from the prompt after the wrap-around the terminal gets completely messed up

### Steps to reproduce

In ZSH export the following prompt customization. And then install Q CLI

```
export PS1="%F{231}______________________ | %F{white}<%?> %F{yellow}%~ %F{white}}
@ %F{green}(mac) %F{cyan}(%n) %F{white}
| => "
export PS2="| => "
export RPROMPT='%F{237}%*'
```

### Environment

```yaml

[q-details]
version = "1.10.0"
hash = "d1552a6c1523a4235fc321a46ec16d0fc5b01c5c"
date = "2025-05-15T23:15:42.473878Z (16h ago)"
variant = "full"

[system-info]
os = "macOS 15.4.1 (24E263)"
chip = "Intel(R) Core(TM) i7-9750H CPU @ 2.60GHz"
total-cores = 6
memory = "32.00 GB"

[environment]
cwd = "/Users/USER/Library/Application Support/amazon-q/shell"
cli-path = "/Users/USER/Library/Application Support/amazon-q/shell"
os = "Mac"
shell-path = "/bin/zsh"
shell-version = "5.9"
terminal = "iTerm 2"
install-method = "unknown"

[env-vars]
PATH = "/Users/USER/.pyenv/shims:/Users/USER/.nvm/versions/node/v18.13.0/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:/usr/local/sbin:/Users/USER/bin:/Applications/iTerm.app/Contents/Resources/utilities:/usr/local/share/android-commandlinetools/bin:/usr/local/share/android-commandlinetools/tools:/usr/local/share/android-commandlinetools/platform-tools:/Users/USER/.local/bin:/usr/local/bin:"
QTERM_SESSION_ID = "329459126a5c40a2a21eb9949c06a710"
Q_SET_PARENT_CHECK = "1"
Q_TERM = "1.10.0"
SHELL = "/bin/zsh"
TERM = "xterm-256color"
__CFBundleIdentifier = "com.googlecode.iterm2"
```