Overview
The Omeka S 4.0.0 release candidate has been published.
https://forum.omeka.org/t/omeka-s-4-0-0-release-candidate/16272
I tried it out on Amazon Lightsail. You can try it at the following URL.
Installation
You can perform the initial setup with the following script.
As of December 15, 2022, the following additional steps were required in addition to the above.
After that, the installation screen will be displayed, just as with Omeka S 3.x.
Features (Selected Highlights)
Resource Page Blocks
It appears that you will be able to customize the layout of item, media, and item set pages. On the following screen, you can change the order of blocks and add new ones.

For example, by adding “Lightbox gallery” to the top of the screen, the Lightbox gallery could be displayed at the top as shown below.

This is expected to make customizing various screens easier in the future.
Configurable Browse Columns and Sorting
Sorting customization has been particularly improved. Specifically, custom fields can now be configured in the following settings screen for each site, enabling initial sorting by arbitrary items.

(Regarding the former columns, I was not sure where they could be configured.)
Advanced Search
More options have been added to the advanced search screen. Specifically, settings related to the presence or absence of images have been added.

Additionally, in the following admin settings, you can configure which vocabularies are used for advanced search. In particular, by setting it to “Used by resources in this site,” only the metadata items used by the items being searched within each site will be displayed as options. This should help avoid the clutter of displaying unused items that occurred in Omeka S 3.x.

Summary
From the limited features I tried, it seems like many things will become more convenient. I hope you find this helpful.