Latest versions of Thunderbird don't store the download history in "downloads.sqlite" anymore, but in "downloads.json".
I have tried the latest CCleaner 5.28 and I confirm it doesn't clean the "downloads.json" file.
The file is not listed in Files and folders in the profile - Thunderbird, but that's because the page is outdated and it's a PITA to get an account to edit a page on this wiki, so it lacks contributions...
I didn't find what version of Thunderbird brought this change, but it's defined in DownloadIntegration.jsm.
Also refs ticket 851466 at bugzilla. Firefox has the change for a few years but again, I don't know about Thunderbird. I only can tell my "downloads.json" had entries more than a year old.