Blog posts pagination not working

The most common problem of similar questions I see on WPSE – contributors confused about template hierarchy.
In your case,
it’s better to check Common WordPress template files section here

These items most important for your question:

front-page.php
The front page template is always used as the site front page if it exists, regardless of what settings on Admin > Settings > Reading.
home.php
The home page template is the front page by default. If you do not set WordPress to use a static front page, this template is used to show latest posts.
index.php
The main template file. It is required in all themes.

So, front-page.php used first, then home.php(if it exists in your theme and Admin>Settings>Reading is set to “Your latest posts”), then index.php.

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