Will Safari ever support WebExtensions api?

Update 2021

The Safari support for WebExtensions was released in 2021 and is available from Safari 14 (shipped with macOS Big Sur). WebExtensions for Safari are published in the App Store. Documentation here: https://developer.apple.com/documentation/safariservices/safari_web_extensions

Original answer

We cannot possibly know this for sure, but Apple is currently not planning to support (a version of) the WebExtensions API. The name of the standard/specification is Browser Extension.

Apple is not part of the W3C group which attempts to make a cross browser standard: https://www.w3.org/community/browserext/participants

For more general info on the Browser Extension W3C working group, see https://browserext.github.io/browserext

The provisional spec can be found here: https://browserext.github.io/browserext/

In macOS Big Sur, Safari will support the WebExtensions API:

New support for the WebExtensions API and migration tools allows developers to bring Chrome extensions to Safari — letting you personalize your browsing experience with new Safari extensions from your favorite developers.