annoying incorrect bashrc version check

### 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 6.8.0-63-generic - Ubuntu 24.04.2 LTS

### Expected behaviour

After q setup and bash integration, everytime I start a new shell there should not be any new version message if I am up to date

### Actual behaviour

After q setup and bash integration, everytime I start a new shell I get
A new version of q is available: 1.12.4

Even though my q version is 1.12.4

Also in a deb install, q is in /usr/bin/q though the pre-bash assumes ~/.local/bin as path. HArmless but unnecessary.

Also in ~/.local/share there are two folders amazon-q initially and Amazon-Q after you launch the desktop client

### Steps to reproduce

_No response_

### Environment

```yaml

[q-details]
version = "1.12.4"
hash = "c20df6ad252618bed22508b33914316ea204af26"
date = "2025-07-09T01:19:17.893407Z (4d ago)"
variant = "full"

[system-info]
chip = "Intel(R) Xeon(R) CPU E5-2697A v4 @ 2.60GHz"
total-cores = 16
memory = "125.70 GB"

[system-info.os.linux]
kernel_version = "6.8.0-63-generic"
id = "ubuntu"
name = "Ubuntu"
pretty_name = "Ubuntu 24.04.2 LTS"
version_id = "24.04"
version = "24.04.2 LTS (Noble Numbat)"

[environment]
cwd = "/mnt/bottomleft/projects/"
cli-path = "/mnt/bottomleft/projects/"
os = "Linux"
shell-path = "/usr/bin/bash"
shell-version = "5.2.21"
terminal = "VSCode"
install-method = "unknown"

[env-vars]
DISPLAY = ":1"
PATH = "/home/USER/.jbang/bin:/home/USER/seb/bin:/home/USER/.local/bin:/home/USER/.jbang/bin:/home/USER/seb/bin:/home/USER/.local/bin:/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin:/usr/games:/usr/local/games:/snap/bin:/snap/bin:/home/USER/.local/bin:/home/USER/.cache/lm-studio/bin:/opt/flutter/bin:/opt/flutter/bin/cache/dart-sdk/bin:/usr/local/go/bin:/usr/local/bin/Telegram:/home/USER/Android/Sdk/emulator:/home/USER/Android/Sdk/tools:/home/USER/Android/Sdk/tools/bin:/home/USER/Android/Sdk/platform-tools:/opt/spark/bin:/opt/spark/sbin:/home/USER/.cache/lm-studio/bin:/home/USER/go/bin:/home/USER/.cache/lm-studio/bin:/home/USER/.config/Code - Insiders/User/globalStorage/github.copilot-chat/debugCommand:/opt/flutter/bin:/opt/flutter/bin/cache/dart-sdk/bin:/usr/local/go/bin:/usr/local/bin/Telegram:/home/USER/Android/Sdk/emulator:/home/USER/Android/Sdk/tools:/home/USER/Android/Sdk/tools/bin:/home/USER/Android/Sdk/platform-tools:/opt/spark/bin:/opt/spark/sbin:/home/USER/.cache/lm-studio/bin:/home/USER/go/bin"
QTERM_SESSION_ID = "b93c377c67ce4854a438df4ecdd0ea0b"
QT_IM_MODULE = "ibus"
Q_SET_PARENT_CHECK = "1"
Q_TERM = "1.7.3"
SHELL = "/bin/bash"
TERM = "xterm-256color"
XDG_CURRENT_DESKTOP = "Unity"
XDG_SESSION_DESKTOP = "ubuntu"
XDG_SESSION_TYPE = "x11"
XMODIFIERS = "@im=ibus"
```

Inizia tracciando il percorso di q setup e bash integration version-check, quindi confronta la versione installata riportata con la versione usata dal controllo e le posizioni degli eseguibili per le installazioni deb e utente. Il lavoro è completato quando un q aggiornato non emette un messaggio relativo a una nuova versione nelle nuove shell e l'integrazione non presuppone il percorso errato dell'eseguibile; analizza inoltre le differenze nei nomi delle directory dati di amazon-q.

Scritto dal modello di indicizzazione a partire dal testo della issue.