shell startup time increased 457% from 0.7s to 3.9s

### 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 15.2.0 (24C101)

### Expected behaviour

Time from starting a new shell instance/tab to time to prompt is not noticeably longer than before Q CLI

### Actual behaviour

Installing Q CLI and now my shell startup time increased 457% from 0.7s to 3.9s

### Steps to reproduce

Install Q CLI

### Environment

```yaml
[q-details]
version = "1.6.0"
hash = "6d13844d6546a5c29e7e121450af1130eb189e7f"
date = "2025-01-09T00:47:39.704258Z (7d ago)"
variant = "full"

[system-info]
os = "macOS 15.2.0 (24C101)"
chip = "Intel(R) Core(TM) i7-9750H CPU @ 2.60GHz"
total-cores = 6
memory = "16.00 GB"

[environment]
cwd = "/Users/USER/Library/CloudStorage/Dropbox/code/conf/dot/aws"
cli-path = "/Users/USER/Library/CloudStorage/Dropbox/code/conf/dot/aws"
os = "Mac"
shell-path = "/bin/zsh"
shell-version = "5.9"
terminal = "iTerm 2"
install-method = "unknown"

[env-vars]
DISPLAY = "/private/tmp/com.apple.launchd.29DJfvdHi9/org.xquartz:0"
PATH = "/Users/USER/.espressif/tools/xtensa-esp-elf-gdb/14.2_20240403/xtensa-esp-elf-gdb/bin:/Users/USER/.espressif/tools/riscv32-esp-elf-gdb/14.2_20240403/riscv32-esp-elf-gdb/bin:/Users/USER/.espressif/tools/xtensa-esp-elf/esp-13.2.0_20230928/xtensa-esp-elf/bin:/Users/USER/.espressif/tools/riscv32-esp-elf/esp-13.2.0_20230928/riscv32-esp-elf/bin:/Users/USER/.espressif/tools/esp32ulp-elf/2.35_20220830/esp32ulp-elf/bin:/Users/USER/.espressif/tools/openocd-esp32/v0.12.0-esp32-20240821/openocd-esp32/bin:/opt/homebrew/bin:/Users/USER/.vector/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:/opt/X11/bin:/Library/Apple/usr/bin:/Applications/iTerm.app/Contents/Resources/utilities:/Users/USER/Library/Application Support/Coursier/bin:/Users/USER/.local/bin:/Users/USER/code/script:/usr/local/sbin:/usr/local/opt/go/libexec/bin:/Users/USER/apps/go/bin:/usr/local/opt/curl/bin:/Users/USER/Library/Python/3.9/bin:/usr/local/lib/ruby/gems/3.0.0/bin:/usr/local/opt/ruby/bin:/Users/USER/.gem/ruby/2.6.0/bin:/usr/local/opt/coreutils/libexec/gnubin:/Users/USER/Library/CloudStorage/Dropbox/code/lib/apache-maven-3.9.8/bin:/Users/USER/.local/bin"
SHELL = "/bin/zsh"
TERM = "xterm-256color"
__CFBundleIdentifier = "com.googlecode.iterm2"
```