Yandex Browser desktop does support manually adding a search engine and making it default.

1. Right-click the SmartBox and choose Manage search engines....
2. In the search engine settings page, click Add.
3. Enter the Queye details below.
4. Save it, then hover over Queye and choose Make default.

Use these details

• Name: Queye
• Keyword: queye.co
• Link with %s instead of the query: https://queye.co/search?s=%s