Password Change Breaks Logout Button

### Expected
When ever I click Log Out in the app I should be logged out and redirected to https://app.simplenote.com/login/

### Observed
Clicking log out in https://app.simplenote.com/settings/ after a password change does not log me out. Instead I am redirected to my notes at https://app.simplenote.com/


### Reproduced
1. Go to https://app.simplenote.com/settings/
2. Click Edit on your password
3. Enter your old and new password and click Change password
4. Click your email in the top right corner to open the drop down menu options
5. Click Log Out

### Where did you see the bug
- System Make: Macbook Pro
- System Model: M1 Max
- OS: MacOS
- OS version: Ventura
- Browser (if applicable): Firefox
- Browser version (if applicable): 108.0.2 (64-bit)
- Simplenote app version:

User reported 5836503-zen

Reproduce the flow from the settings page at https://app.simplenote.com/settings/ by changing the password, then use the account menu's Log Out action. Trace the logout behavior from that entry point and compare it with the expected redirect to https://app.simplenote.com/login/; done means logout after a password change redirects there instead of the notes page.

Written by the indexing model from the issue text.