Adding something to a table will depend on what or how the table is made.
If the table was from a shortcode and is not editable through Gutenberg (the Block editor), then you’ll may have to check the code that created the shortcode if it has any hooks that you can use to add in things like buttons.
If it’s some sort of a Table block that can be edited within Gutenberg then adding contents like buttons should be a simple drag and drop.
To get more context so I can provide a more helpful tip, can you link us to the page with the table? So I can observe it and find clues on how you can add your button to it. 😀
A wise man once said:
"Have you cleared your cache?"
I have not yet published the article so I don’t have a URL.
I added a “table block” and then created a “button block”. I tried to drag and drop the button into the table but it won’t work. I also tried to copy and past it into the table but that was also unsuccessful.