App Version: 72.0.3610.0 Canary
iOS Version: 11.4.1, 12.0.1, 12.1.1 beta #2
Device: iPhone and iPad                                                                                                                                                                                                                                                                            

Pre-requisite: Enable custom search engine flag from chrome://flags

Steps to reproduce:
1. Launch chrome
2. Visit any of the search engine websites (eg: github.com) and perform a search
3. Go to search engine in settings
4. Select GitHub 
5. Trigger clear browsing data
6. Go to search engine in settings

Observed results:
Notice that Github is not removed

Note: The unselected custom search engines are removed on triggering clear browsing data.

Expected results:
All custom search engine should be removed on triggering clear browsing data and Search engine should be set to Google as default

Number of times you were able to reproduce: 5/5
Bug reproducible after clean install: Yes
Bug reproducible after clearing cache and cookies: Yes
Bug reproducible on Chrome Mobile on Android: No on Android in M71
Bug reproducible on Safari/Firefox: Firefox: NA, Safari: NA
Bug reproducible on current stable build (App Version, iOS Version): NA on M70 (Feature is new from M72)
Bug reproducible on the current beta channel build (App Version, iOS Version): NA on M71 (Feature is new from M72)

Link to Video:
https://drive.google.com/file/d/1eM5qjFS8viZc2XiMfxhLC-UyyEyTcgU3/view?usp=sharing