To generate those dropdowns which are links to the alternate category or tag archives you must generate the markup for them yourself, the select inputs and options, but naturally you'll want to do this dynamically.
You'll need to create a taxonomy View for each, one for categories, one for tags, and in the output section add a select input tag outside of the wpv-loop tags with the option tags inside the loop, using shortcodes for the term URL (for the href attribute of the link) and for the term name for the link text.
Note that Blocks doesn't support taxonomy Views yet, you'll need to use the legacy Views UI to create taxonomy Views. If you are using Blocks to create the custom archive, to be able to insert the taxonomy Views you'll need to use the Classic block (which has the Fields and Views button available behind the Toolset icon) or enter the wpv-view shortcode into a Shortcode block directly.
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