And it's impossible to get rid of it changing manually in HTML. Every time I'm updating created Button block it automatically changes back.
The padding is added because of the "Button" content type - the WYSIWYG has essentially locked down what you can truly edit.
I would recommend copying that code and creating a new content block as "Free Form" or "HTML", pasting that code and then making your edits. This should enable you to make edits freely without the defaults of that content type overriding your customization.
Note that if you choose "Free Form" you will still have some WYSIWYG capabilities when editing but if you choose "HTML" you will only be able to work with raw HTML - no WYSIWYG elements will be available for that content format.
That is a bug that is currently targeted to be fixed in the June release.