My web extension works with Chromium browsers, Firefox, Edge, but as I understand - it is impossible now just to open the same codebase with Safari browser?
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/