About formatting nice table in HTML, know that there was a discussion on several options.
Could be of interest to you.
For KableExtra, did you read the website ? you could find what your looking for. There are examples for full width table where column size is adapted, not full size table and also how to fix width with column_spec.
Without more information on what you want to do, it is difficult to not guess what you want. If you could provide a reproductible example of what you try, it will help us help you.