1 Correct answer
I finally got around to upgrading, and I can confirm that CC2019 fixes this bug. (Windows is still on 1803, so that's irrelevent, as I suspected.)
CC2019 also solves another annoyance that I had off-and-on considered complaining about - InDesign previously was the only Adobe software I use regularly that would always open on my laptop monitor instead of my external ultra-wide monitor I use it on. But CC2019 opens on the same monitor, location, and size as when it was last closed, just like it sho
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Hi OsakaWebbie,
Please check which application is the default application for PDFs.
Strat Menu > Settings > Default apps > Choose default apps by file type
Scroll to .pdf and check which application is selected as default application if it is InDesign change it to Adobe Reader or Adobe Acrobat reader.
Regards,
Srishti
Adobe Acrobat DC is the default application and always has been so.
Looking at the Recent list again now, it's even weirder - it almost seems random. I'm seeing recently exported PDFs (perhaps all of them - I'm not sure), recently placed image files (some, not all), and a couple INDD files (some, not all). Here is an annotated screenshot of my current list:
As I said, I also have InDesign CC2017 Japanese, which I installed in February this year when I discovered that the English version didn't create the right kind of printer marks for Japanese printshops. I just now looked more closely at its recent list and did some testing (shown below). Although it has only INDD files (I exported a PDF just now, and it did not appear), it also has other mysteries. Only four of the files were actually opened in that version - the top two were today's test (a Save As and an Open) and the next two were in February. The rest were only opened in the English version! Most are older (from before I upgraded the English version from 2017 to 2018), so it's logical to assume that it adopted a list that was present on the system. But notice that two of the icons are different from the rest (I pointed at them with yellow arrows) - those are CC2018 files, and I think the rest are CC2017 (from before I upgraded the English installation). And neither of those icon types look like the white-bordered icon showing for all files in the above list. The fact that the icons in the above list are all the same for five totally different types of files is also an indication that something isn't working right.
Do these clues help you figure out what might be going on?
One more screenshot - to prove that inside CC2018 everything looks as it should. Both on the opening view and in the menu item File->Open Recent, all the INDD files I have opened recently appear. There is one PDF at the bottom of the list, but it's possible that I did try to open that one as an experiment - I don't remember.
I have now noticed that other Adobe software has the same problem, and the version delineation is also less clear, as most of my programs are still the 2017 version. I see imported resource files in all of these lists, and exported results in most of them (Premiere Pro is the exception, but it uses Media Encoder for output). It's weird that InDesign 2017 Japanese doesn't do it - it shows only files that were opened.
I did what I could to test non-Adobe software. Everything I use except Adobe and MS Office are "portable" versions, so they don't store anything in the registry, and MS Office has very little capability of merely exporting - in most cases Save As ends up with the new file format opened in the software, which would naturally put it in the Recent list. But an exception is PDF - it is a true export (because Word can't even open a PDF as far as I know), and the resulting file does not appear in the Recent list. Before the screenshot below, I opened an existing Word document and saved it as TXT and PDF, and only the TXT (which had become the currently open document) showed up on the Recent list. So the limited evidence is still that only Adobe software has the problem.
It seems like it's getting worse. I was previously able to mitigate it by pinning current projects to the "jump list" for the InDesign tile, but as far as I know I can only pin something when it appears in the Recent list. The INDD file for the current issue of the magazine I design, which I have been opening and closing repeatedly for the last month, has never shown up in the list at all. I tried deliberately opening it from File Explorer (well, technically Directory Opus, but it interfaces with Windows the same way as far as I know), deliberately opening it from inside InDesign, saving before closing, just closing immediately, and various other combinations. The only files that show up in Recent are placed images and exported PDFs - here is a screenshot after I had opened and closed several InDesign documents entitled "JH [something].indd", which you can see are not showing at all:
If you know of a way to pin a document to the InDesign jump list without seeing it in Recent and clicking the pushpin icon, I'm all ears. And of course I'd also like to actually solve the underlying problem of the Recent list.
Anything more on this?
Here's a screenshot showing my current list of irrelevant files (the "Sponsor Cards" one is an INDD file I opened once just to look at something; the rest are placed or exported files related to the magazine document I want to pin), showing what I meant by pinning a document to the jump list. If the document I want to pin never appears in "Recent" due to this mysterious bug, is there a different way to pin it?
Haha, I'm already old... but I'm not dead yet! 
I wasn't suggested that CC2018 be fixed. But no one has said that CC2019 fixes this problem. Does it?
Naturally I will upgrade at some point, but I don't tend to be in a hurry to upgrade any software if I'm not aware of something new that I need. I rarely utilize the latest features, sometimes things change enough to require a learning curve (e.g. I still struggle with the MS Office "ribbon" - I can't find things I know exist, and having to use Office in Japanese makes it harder), and I've been burned by irreversible upgrades that wouldn't work (even in Adobe CC, where I can theoretically reinstall anything - seeDolby codec issue on Windows 10).
I finally got around to upgrading, and I can confirm that CC2019 fixes this bug. (Windows is still on 1803, so that's irrelevent, as I suspected.)
CC2019 also solves another annoyance that I had off-and-on considered complaining about - InDesign previously was the only Adobe software I use regularly that would always open on my laptop monitor instead of my external ultra-wide monitor I use it on. But CC2019 opens on the same monitor, location, and size as when it was last closed, just like it should. 
I have this same issue in InDesign 2020. Prior to 2020 I would regularly right-click on the INDD task bar icon to open a recently opened file, but now it shows me all file types and I am so used to using it, I consantly attempt to open PDF files by mistake. This is so odd. All of my default application are set for what it keeps showing me in this list.
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