Couple of thing as one who deals with 1,000+ 404s in Google Search Console at any one time and also dealt with leaky CMS systems.
A) Dealing with 404s in Google search console
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Small thing, if these pages are gone and 404 and will not come back, consider showing a 410 (permanent gone) vs a 404, but either will work.
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Make sure you have a useful 404 page when people land there so that they can go somewhere else if they need.
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VERY IMPORTANT - DO NOT mark a 404 as "fixed" in Google Search Console, if the page is supposed to 404.
Why? Because if the 404 is fixed, then Google will expect to see a 200/ok response! It will then say, "Oh, the webmaster said this was fixed, but I still see the 404 so I will put it back in the 404 report to help this webmaster." You will then see the 404 show back up in your console after you removed it and then you start that weird eye twitch that you get when you start to stress. In fact, I have found if I ever marked a page that is supposed to 404 as "fixed" it takes it that much longer to get out of the 404 report.
What search console needs is a way to mark a 404 in the crawl report and say, "Yep, I see it and it is supposed to 404" in addition to the "Fixed" option.
Rule of thumb, if the page is supposed to 404 let it 404 and just ignore it in the crawl errors of Google webmaster tools / search console. You do not need to "fix" anything. The 404s will drop out after about 3 months. I just check the 404s and then sort by date to see the newest. If they are supposed to 404 (see point below) I leave them alone and don't stress.
All the other stuff about removing URLs is usually a waste of time. Just let Google do its work.
If you don't believe me, just ask Google
http://googlewebmastercentral.blogspot.com/2011/05/do-404s-hurt-my-site.html "If some URLs on your site 404, this fact alone does not hurt you or count against you in Google’s search results."
https://www.seroundtable.com/google-panda-404-20738.html "Google's Gary Illyes responded in short to a Google Panda question, asking if having 404ed pages have an impact on the overall Google Panda algorithm. Gary said on Twitter, "nope," it does not.
https://support.google.com/webmasters/answer/2409439?hl=en Google's webmaster docs _"_Generally, 404 errors don’t impact your site’s ranking in Google, and you can safely ignore them."
All of the above assumes that these are pages that are supposed to 404. In other words, they are pages that you did not try to use for ranking, etc. If these were important pages, like home pages or landing pages, then sure a 404 is bad it would negatively impact ranking of those pages. Good pages you want to fix, yes. Bad pages, just let them die and remove links to them as well for a good user experience.
B) Dealing with leaky CMS systems
I know this may not be your case right now, but it seems to have been before and so wanted to toss this out there as well. Somewhere, there is (or was) a link to these drafts you mention that are out in the public. You need to search Google, look through Moz or Majestic or use Screaming Frog to find how these drafts got linked to. If you look in search console, you should be able to click the 404 errors and see where they are linked from as a clue.
Until you fix the leak, you will end up with wet shoes every time. Here is an example of where a person was using custom code to display posts, and the code was showing draft posts by accident: https://wordpress.org/support/topic/draft-posts-showing-up-in-recent-posts-feed
Hope this helps!