`bash` with shell integration on triggers `.bashrc` update with `shellStartup`

If shell integration is on and it supports activation, then we should not be triggering `.bashrc` update.

<img width="2570" height="1542" alt="Image" src="https://github.com/user-attachments/assets/49ed8091-efac-4520-8ffb-ef64768ce79a" />

<img width="3116" height="1560" alt="Image" src="https://github.com/user-attachments/assets/f3ed4355-8fa2-429b-bd86-9b4032e581a6" />