Hello Ivan
I'm not too familiar with Beaver Themer and the various Beaver extensions you have, and I don't have the time to dig deeply to see exactly how they are working on your site.
Instead I have created a demo site for you to see how this works without the distraction of Beaver, and I'll leave it to you to weave Beaver back into the mix.
So, here is the site: hidden link
You can log in to the admin pages with that link, no username/password required.
Now, I imported the sample WooCommerce content for the purposes of the demo.
I'm not worried about the design, just setting the workflow up with simple links.
If you visit the home page you will see it includes a View to display links to the top-level product categories.
On this demo site, only clothing has sub-categories, so test with that link.
That will take you to a custom archive for product categories.
At the top I have inserted another View, this time to display links to the sub-categories.
Beneath that appears the results of the archive, i.e. the list of matching products. Importantly, this is the WordPress archive for product category results itself, i.e. the main query on this page, not some other View we added with a custom query.
You'll note the pagination links. I've added Views pagination links, and I have left the theme pagination links.
They both work, but there are important differences.
The theme pagination links are "standard" pagination links, so they will work nicely with other 3rd party products, where relevant.
So why bother with Views pagination links at all? Well, you would need to if you are using Views custom search filters. The theme pagination isn't aware of them, and the standard pagination won't respect the filter results.
But if you are not using Views search filters, then you could just use the theme pagination links.
I also installed your product filter plugin and added its widget (to the footer).
You should be able to see that, because we are displaying products through the main query for the archive page and not some custom Views query, then its filters work. And, they work in combination with the theme's pagination links.
But they don't work with the Views pagination links, which is expected.
Now, you have issues with Views pagination links on your site even when the filter plugin is disabled, but I think that is to do with how you have set this up, including using Beaver to generate the archive.
If you study my sample site to see it working I think you should be armed with enough to try and implement the same on your site, even with Beaver, but if you run into a specific, replicable issue where Beaver (or one of the various extensions) breaks the pagination, then let me have the details and if I can reproduce I can escalate for it to be debugged and fixed.