Rollup merge of #115988 - notriddle:notriddle/search-tab-layout, r=GuillaumeGomez

rustdoc: add test cases, and fix, search tabs layout jank

## Before

### Resizing

https://github.com/rust-lang/rust/assets/1593513/24bb5f2b-f6bd-4ed8-91e1-f9ff63d1acee

### Typing

https://github.com/rust-lang/rust/assets/1593513/145f53e1-42eb-4b2a-adba-7c9ab44b0aa4

## After

### Resizing

https://github.com/rust-lang/rust/assets/1593513/acc10a55-e83e-43e6-8604-5dfcb9ae3141

### Typing

https://github.com/rust-lang/rust/assets/1593513/09d6d389-e24f-428f-933f-83d9075f15a2

Author: GuillaumeGomez