I would also find it useful to have access to this information for an individual pull request via the API, so that I can collate a list of all the open PRs that need attention across a number of repos.
This is definitely a pain point right now, when people have to review multiple PRs it becomes really hard to be sure of what PR is actually ready to merge and what requires action. The fact that the API doesn't support any way of fetching conflict status for a PR makes things even harder because we cannot even write an extension for that.
This is the second thing on my team's list for PR effectiveness right after issue #4954 which I understand is going to be fixed.
The fact I have to go into each and every PR to know the status makes the PRs list page literally unusable to me other than knowing which PRs exist.
But I don't understand why this issue is of type "proposal". To me this is a bug.
The tests column is green but there's a conflict?
Looks like a bug to me.
And if possible, I would go beyond just showing conflict or not, I would add a button to update with target branch.
That would make the PRs page very useful for managers / team-leaders.
And the button will have to show me if there will be a conflict or not.