Basically you have two problems.
The content of a button must be short
A button isn't made to have large contents inside it, and the fact that the button is standard <button> or faked with ARIA role=button doesn't change anything (for screen readers and other assistive tools, both appear the same for the user at the end, that's precisely the purpose of ARIA).
Remember that the whole content of the button is read in one go by the screen reader when it is focused, makes a giant label in a list of buttons to click on, and also that you might need to speak aloud the whole content to activate it with voice control.
It's unclear which action a click performs when a lengthy content is read with a lot of information. Does it open a page with more details ? Is the product directly added to cart ? Does it immediately launch a rocket missile without any other confirmation ?
Even if the actual action performed is written in clear somewhere in the middle, it is flooded by all the rest and so unoticible.
Therefore, the content of a button has to be short, directly telling what's going to happen if you click, otherwise it is, practically speaking, not accessible, or excessively painful to use.
Nested interactive elements
You can't simply say that a button can have arbitrary content. You should prevent that, or change completely your design.
In fact, as soon as you have another interactive element inside your button, you are running into issues. This is well known as the nested interactive zone problem, which must be avoided at all cost.
- When pressing enter or clicking on the inner element, should the outer element also be triggered ?
- When focusing the outer element, should the content of the inner element also be read by screen readers ? usually it is and it creates a lot of confusion because some content is read twice, or what is read doesn't correspond to the performed action
- Visual focus indications might be unclear as well
- You can easily click by misstake slightly outside the inner element, and trigger the outer element instead while it wasn't intended
- When the mouse is inside the inner element, do you consider it to be inside or outside the outer element ?
- etc.
All these questions haven't a definitive clear answer. Sometimes you would prefer an answer to be yes, and sometimes no. It's difficult and not recommended to go against default behavior. It could be different with different browsers/OS/etc.
A fully clickable card isn't a button
As you should have now understood, your fully clickable card shouldn't be considered as a button. You should neither use <button>, <input type="button"/>, nor role=button tabindex=0. All are WRONG!!!
Even if you prevent nested interactive elements by any mean, the length and flood of information given by a single card read as a whole is still a problem
A possible solution could be to keep the entire card clickable as it is now, but don't make it focusable. However, be very cautious, because by doing so, it's no longer accessible to screen reader and keyboard only users, among others.
You have to provide an alternative mean to open the card. You can, very simply, add an explicit "More details" link or button somewhere, or use the title of the article as a link, etc.
See for example this question and the linked article.
The card in the example stays fully clickable, but screen reader and keyboard only users interact with an heading link, which is the title of the article.
This could be a solution for your case, too.
<button>children rules were relaxed<a>tags on the other hand permit just about anything. What is the reason behind not considering an anchor?