[PM-24511] Inconsistent UI/UX for vault sync

### Steps To Reproduce

The "Sync now" button on iOS app is under Settings->Other instead of Settings->Vault. On the browser extension, it is found under Settings->Vault options. This is inconsistent and also confusing when using both.

### Expected Result

"Sync now" button in same location as other Bitwarden applications/browser extension.

### Actual Result

"Sync now" button in a different location.

### Screenshots or Videos

_No response_

### Additional Context

_No response_

### Build Version

2025.7.0 (2278)

### What server are you connecting to?

Self-host

### Self-host Server Version

2025.7.2

### Environment Details

iPhone 14 Pro
iOS 18.6

### Issue Tracking Info

- [x] I understand that work is tracked outside of Github. A PR will be linked to this issue should one be opened to address it, but Bitwarden doesn't use fields like "assigned", "milestone", or "project" to track progress.

Start by comparing the iOS Settings > Other and Settings > Vault locations with the browser extension's Settings > Vault options. Trace the iOS settings entry points for the "Sync now" action. Done means the button is located consistently with the other Bitwarden applications and remains usable on the reported iOS environment.

Written by the indexing model from the issue text.