CustomActions that deploy script, JSLinks, and additional web parts on the page are currently not supported in the new experience. Environments that require these unsupported features should continue using classic mode for the time being.
Affected Software Versions
This functionality is introduced gradually to organizations that have opted in to the SharePoint Online(SPOL) First Release program. This means that you may not yet see this feature immediately as the change is being pushed by Microsoft User by User.
Fix / Resolution
Microsoft is working on the long term plan for this. It does not mean that Microsoft would not support this in future. Microsoft is looking for few different options around these kind of customizations, but unfortunately plans have not yet been locked, so Microsoft can’t share exact final outcome yet.
Interim Workaround
Document Library Level
Flip the impacted document libraries back to classic mode via Library Settings -> Advanced Settings (or in a more heavy-handed approach to configure the classic mode at the tenant level).
Site Contents Page Thankfully (for now at least) Microsoft gives us a link in the lower left-hand corner “Return to classic SharePoint? that will revert the experience back to the same old lovable customizable SharePoint experience. Tenant level single switch to turn on the classic mode is not available for Site Contents Page.
References
https://veenstra.me.uk/tag/return-to-classic-sharepoint/
You can see the product group response in this user voice request: https://sharepoint.uservoice.com/forums/329214-sites-and-collaboration/suggestions/13385364-allow-javascript-customization-and-css-branding-th and vote
https://www.yammer.com/itpronetwork/#/Threads/show?threadId=721245585