[PM-43607] Ask to Save constantly popping up on iOS recently

### Steps To Reproduce

1. Go to a website in safari that has a saved password (https://www.royalroad.com/for instance)
2. Click on username field to login
3. Autofill using account identified in top row of keyboard area (from bitwarden, identified correctly for the site)
4. Click login (success)
5. After login a modal pops up asking if I want to save

### Expected Result

I should not be bothered with a modal popup to save a password that was just autofilled from bitwarden. It's obviously working and correctly identifies the site.

### Actual Result

I get a popup every single time from sites that were just autofilled by bitwarden

### Screenshots or Videos

_No response_

### Additional Context

_No response_

### Build Version

© Bitwarden Inc. 2015–2026 📝 Bitwarden 2026.8.1 (3489) 📦 Bundle: com.8bit.bitwarden 📱 Device: iPad16,5 🍏 System: iPadOS 26.6.1 🦀 SDK: 3.0.0-7742-9794da5 🌩️ Server: 2026.8.2 @ US 🧱 Commit: bitwarden/ios/release/2026.8-rc56@dede418b15642365dca3600452dbbef6748bd640 💻 Build Source: bitwarden/ios/actions/runs/32510537668/attempts/1

### What server are you connecting to?

US

### Self-host Server Version

_No response_

### Environment Details

ipad, iphone, ios 26

### 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 issue on the reported iPadOS and iOS versions using the Safari autofill flow described. Trace the iOS autofill and save-password entry points to determine why a successful Bitwarden autofill still triggers the save prompt. Done means the prompt no longer appears for passwords just autofilled from Bitwarden, with regression coverage for the reported steps.

Written by the indexing model from the issue text.