Quick search engines bar covers keyboard and does not follow keyboard height correctly

[eqilnou]

Description

The quick search engines bar does not change position following a change of height of the keyboard or a switch from landscape to portrait mode, and ends up covering the keyboard (or being too high up).

Moreover, without any change to the keyboard height, the quick search engines bar covers key popups from the keyboard.
Additionally, the bar also covers the system prompt for changing the input method.

Steps to reproduce

1. Open a new tab and start typing in the search bar, so that the quick search engines bar appears on top of the keyboard
2. To reproduce the first issue: rotate the device to landscape mode and then back to portrait mode. Alternatively, cause the keyboard to change height in a different way, such as by enlarging or collapsing the keyboard smartbar, or by changing the keyboard height from its settings. Alternatively, switch to another keyboard that has a different height.
3. To reproduce the second issue: after step 1 open a keyboard popup which exceeds the height of the keyboard
4. To reproduce the third issue: after step 1 tap on the button on bottom of the screen for changing input method

Actual result

1. The quick search engines bar is now no longer in the correct position, but is either too high (if the keyboard height decreased) or too low and covering the keyboard (if the keyboard height increased).
2. The bar covers the popups of the keys of the keyboard.
3. The bar covers the system prompt to change input method. (Note that I have also tested some other system prompts, and none of them were covered by the search engines bar).

See screenshots below.

1. After changing from landscape to portrait:
   

2. Opening popups:
   

3. Attempting to change input method:
   

Expected result

1. The quick search engines bar follows the keyboard's height's changes.
2. The bar does not cover the popups of the keys.
3. The bar does not cover system prompts.

Reproduces how often

Easily reproduced

Brave version

1.79.123

Device

• Brand/model: Google Pixel 5a
• Android version: 14

I can also reproduce all described behaviour on an older device:

• Brand/model: Huawei P8 Lite 2017
• Android version: 8

Channel information

• release (stable)
• beta
• nightly

Reproducibility

• with Brave Shields disabled
• with Brave Rewards disabled
• in the latest version of Chrome

Miscellaneous information

Potentially related issue: #42254

Note that I tested multiple keyboards and the issues reproduce on all of them.
Also, the issues reproduce regardless of whether PiP permission is enabled or disabled.

I think that there are two issues: one is the failure to dynamically adapt to keyboard height changes, the other is that the bar covers the keyboard/popups/prompt. I think that the second issue is, at least partially, an issue of the operating system, since it should disallow apps from overlaying content on top of input methods and system prompts: it shouldn't be up to the apps to do this.
So I think it should be reported to AOSP if someone reproduces this on the latest Android version.