[PM-40081] Fails to connect to server to update, sync, etc. with Cloudflare Zero Trust protection enabled

### Steps To Reproduce

**System**
1. Android device
2. Cloudflare Zero Trust protection profile enabled
3. Open Bitwarden
4. Get an error occurred.

Vault unlocks and can be used for stored passwords, but cannot update passwords, save new ones, etc.

### Expected Result

App works like normal including syncing and saving new items or updates.

### Actual Result

App provides "an error occurred"

**Desktop**
Both the desktop version Bitwarden (MacOS) and website at vault.bitwarden.com work normally when Cloudflare is enabled

### Screenshots or Videos

_No response_

### Additional Context

I ran flight recorder with Cloudflare on and tried to sync the vault and start a new login type. Then, I turned off Cloudflare and ran the same actions.

[flight_recorder_2026-07-07_12-45-22.txt](https://github.com/user-attachments/files/29755334/flight_recorder_2026-07-07_12-45-22.txt)

### Build Version

2026.6.0 (21686)

### What server are you connecting to?

US

### Self-host Server Version

_No response_

### Environment Details

Device: Pixel Pro 9
OS: Android 16
Cloudflare Client: 2.5.3 (5275)

### 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 reproducing the sync and new-login failures on Android with Cloudflare Zero Trust enabled, then compare the attached flight recorder output with a run where Cloudflare is disabled. Done means the app can sync the vault and save new or updated items while protection remains enabled.

Written by the indexing model from the issue text.