I Googled "windows 10 delivery optimization logs" and found https://petri.com/troubleshoot-windows-update-delivery-optimization which led me to its PowerShell commandlets.
After some experimentation, I executed Get-DeliveryOptimizationStatus -Verbose | Format-List Status,Priority,SourceURL,DownloadDuration,TotalBytesDownloaded which outputted the following:
PS C:\WINDOWS\system32> Get-DeliveryOptimizationStatus -Verbose | Format-List Status,Priority,SourceURL,DownloadDuration,TotalBytesDownloaded
VERBOSE: Perform operation 'Enumerate CimInstances' with following parameters, ''namespaceName' = root/Microsoft/Windows/DeliveryOptimization,'className' = MSFT_DeliveryOptimizationFile'.
VERBOSE: Operation 'Enumerate CimInstances' complete.
Status : Caching
Priority : Foreground
SourceURL : https://clientupdates.dropboxstatic.com/dbx-releng/dropbox_passwords/win/DropboxPasswords_beta.appinstaller
DownloadDuration : 10:14:42.1920000
TotalBytesDownloaded : 50549400
Status : Paused
Priority : Background
SourceURL :
DownloadDuration : 00:00:00
TotalBytesDownloaded : 0
Status : Downloading
Priority : Foreground
SourceURL : https://clientupdates.dropboxstatic.com/dbx-releng/dropbox_passwords/win/DropboxPasswords_1.1.27.appx
DownloadDuration : 16:13:46.5660000
TotalBytesDownloaded : 70817815424
PS C:\WINDOWS\system32>

I expected to see something related to Microsoft, not entries solely related to Dropbox Passwords, one of which being a download that's lasted 16+ hours and downloaded 65.95 GB! The entire app is only supposed to be 161 MB!

Dropbox Passwords aligns with the timeline as I installed it on the day of announcement (2020/08/12) or the day after (2020/08/13) which I roughly recall is when this problem started.
I uninstalled the app via Settings → Apps → Apps & features but the issue didn't subside and Get-DeliveryOptimizationStatus still reported the same.
I rebooted my PC and found that:
- The problem had almost entirely subsided. The process is still running but it's now only consuming ~12 % of the CPU which may well be normal.
- For the first few minutes,
Get-DeliveryOptimizationStatus reported no activities.
- After a few minutes,
Get-DeliveryOptimizationStatus reported two activities, both Dropbox Passwords but both paused.
- Settings → Apps → Apps & features reported that Dropbox Passwords was installed again so I uninstalled it again.
Get-DeliveryOptimizationStatus is still reporting all activites paused.