I've been using access with the whole toolset suite for a few months. I use access only for its "publication groups" that I assign to some pages. I never used it for "post types", and therefore all post types are set to "not managed by Access". I want it to stay like this.
In backend, admin, editor and author did add and edit new post types, but since last update, and even if the Access settings did not change, only admin may add or edit posts...
This change does relate to a bug in Access, but it was the prior behaviour that was a bug and the changed behaviour is the bug fix.
It was listed in the changelog for Access 2.4: "Fixed an issue about post group dialog, in order to exclude post types that are not managed by Access."
I'm afraid you will need to manage the relevant post types with Access to be able to use the post groups.
I'm sorry if it is causing issues with your site, but the previous implementation contained a bug which the new version fixes.
You are not generally obliged to manage post types with Access, which is why the "Not Managed by Access" setting exists. You are only obliged to manage a post type with Access if you want to control access to individual posts of that type inside a post group.
If you wanted to control the "Hello World!" post using an Access Post Group then 'posts' need to be managed by Access. You can have different settings for the post type and for the post group, so for the post types which you have to bring under Access control you should just be able to use the defaults and then not experience any difference.
What are the Access settings for standard posts, pages, and your custom post types?
In the screenshot, for example, you can see I am managing the Projects post type with Access and that the Editor role has rights to do everything except "Preview any", which are the default options.
Then it appears there is something wrong with your installation, yes, because that should not happen like that and it is not what I see on my local test site.
The next step will be for me to request a duplicate of your site for testing locally, but before I do can I just ask you to rule out conflicts arising from other plugins or your theme.
Disable all non-Toolset plugins and see if the editor can edit posts, and also try switching theme to twentyseventeen and try again.
Thanks for providing access to the site. I was able to observe the problem.
Upon testing further I found that the culprit seems to be a conflict with... WPML. De-activating WPML seems to resolve the problem.
I'm escalating this to second tier so they can investigate further and test whether this is an issue specific to your site and settings or a bug that will affect all users.
I've taken a duplicate of your site to pass on to them.
I checked the internal tickets for this which show that, yes, the bug is escalated to the developers but, no, it is not resolved yet.
You should be able to work around the problem by bringing your Depeches post type under Access control and granting Editors the permissions required. The bug specifically affects permissions when Access is not managing the post types.
I will update here when there is progress reported by the developers.