App Version: 72.0.3626.31 Beta
iOS Version: 11.4.1, 12.1.1, 12.1.3 beta#2
Device: iPhone and iPad                                                                                                                                                                                                                                                                  

Steps to reproduce:
1. Launch chrome 
2. Go to chromium.org
3. Enter any keyword in search field and tap on the ‘Search this site’ button
4. Go to Settings>Search Engine 

Observed results:
Notice that chromium.org is not displayed in recent visited list

Note: if the search is performed using the device keyboard then the chromium.org is displayed in recent visited list

Expected results:
Chromium.org should be displayed under recent visited list

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 Chrome Desktop: No
Bug reproducible on Chrome Mobile on Android: No
Bug reproducible on Safari/Firefox: Firefox: NA, Safari: NA
Bug reproducible on current stable build (App Version, iOS Version): No on M71 (Feature is available from M72)
Bug reproducible on the current beta channel build (App Version, iOS Version): Yes on M72 Beta

Link to Video:
iOS behavior:
https://drive.google.com/file/d/1QzWOh7yRF29IC_LXra3ffck-ra6Yqpfl/view?usp=sharing

Android behavior:
https://drive.google.com/file/d/1Sv_XP_PjGCItVizFJAS_H_3JrK2eVrV8/view?usp=sharing