Variant options and customization when out-of-stock

How to enable selection/viewing of sold out product variant?

When a product is sold out, it is unable to be selected so customers are unable to see prices of a specific product variant.

Additionally, native Shopify restock requests only allow for reference to the product page, not the specific variant SKU. Is there any way to change this or is a plug-in/custom script needed?

For that either you can turn on the checkbox which says continue selling when out of stock.

Or if you want to just show prices and not take orders, that is doable with css, so Shopify adds a class to sold out items, we just need to remove the class or set display to block from none.

As for the second request I don’t really understand it

Best

This is theme-dependent. Some themes allow selection of sold-out variants, some do not, some has a switch for this.

Also – what’s “native Shopify restock” – a contact form shown instead of the ATC button?
Yes, it’s possible with custom JS, but need to see your store to suggest anything.