Steps to reproduce:
1. Open an existing project or create a new one
2. Open Animator window (Window -> Animation -> Animator)
3. Create an Animator Controller in the Assets (Create -> Animator Controller)
4. In the Animator window switch to Parameters tab
5. Add a new Int parameter
6. Click on the search field while still in the parameter name selection mode

Expected results: Name selection mode is saved to it's current state and exited
Actual results: Name selection stays active when clicking on the search input field

Reproducible with: 2019.4.36f1, 2020.3.29f1, 2021.2.13f1, 2022.1.0b10, 2022.2.0a7

Notes:
- In 2020.3 this seems to reproduce with all parameter types