I want to search by SKU but suggestions don't appear.
For example, most SKU start by "600", the ajax request made by Magento 2.x is:
The result is
SKU field is searchable and active, why does it return 0 results?
Those search suggestions by default are based on what previous users have searched.
In admin if you go Marketing > Search Terms, you have a list of all of them. If you go into a specific one, you have a control "Display in Suggested Terms" - Yes or No, to block the ones you don't like being displayed there.
So just try searching for some of your 600... SKUs a few times and see if they start popping up in the suggestions.
You can clear your Magento cache to refresh search results and potentially resolve the issue. Sometimes, third-party extensions can interfere with search functionality. Disable extensions one by one to identify any conflicts.