Perhaps
http://voidtools.com/support/everything/ would interest you, I now use it all the time and my mind is blown by the fact that NTFS and (ReFS) has these features but Microsoft doesn't expose a nice GUI for them... I seriously consider looking into replacing my start menu with something that'd be much more fit for me personally, scriptable in Lua and query from everything daemon instead but I have no idea how feasible or easy that'd be but classic shell is a thing so it's clearly technically possible (I think, unless it's a dirty hack).
Another fix could be putting a shortcut to the exe (named what you want) into C:\Users\YOUR-USERNAME\AppData\Roaming\Microsoft\Windows\Start Menu\Programs, for me these seem foolproof.
However I'm similarly flabbergasted with what's going on in the start menu search (which I assume is part of Cortana since this is where her blue ring appears after clicking the home shaped icon): I type in 'downloa' and I get option to search the web (in Bing in Edge of course, despite my default being Firefox + Google) and/or 'Download maps for offline use', 'Delete downloaded maps', 'Windows Defender settings', 'Windows Defender security center' (all are built in Windows things) and after few seconds (and my Windows is on an SSD) it seems to catch up and detect the Downloads folder (that comes standard with English Windows install and isn't in any deep or hidden spot...). I add one more letter and get 'download' and the same happens but Edge online search is available only for a split second.
And then the finale: having 'downloads' (or 'Downloads', not that Windows is sensitive even if NTFS deep down can supposedly be set to be) in there looks like this: https://imgur.com/a/Jlhno I have no idea WTF just happened to have the actual Downloads folder as third result after Microsoft Store (?!) and online search with Bing in Edge (sigh...) and hidden in a sub-menu after looking for literally 'downloads'.
Another funny thing is that for me searching for 'Notepad' matches Notepad++ first and Windows built-in Notepad second. I'm not exactly unhappy about this one but it's weird, it might be heuristics but then why doesn't it work heuristically for the 'downloads' search and gives me the store I never used instead of the folder I access daily?