Uploading Time Machine backups.backupdb to cloud service?
You will not be able to backup/copy all or part of your Time Machine (TM) backup to the cloud in a form that would allow recovery from the cloud to recreate a TM 'backup'.
But, I have a few suggestions on how to proceed.
For an 'archive' (a point-in-time copy which will remain untouched for a long time) you can copy folders from your Mac to a cloud service like an AWS bucket.  The folders you copy could be directly from your active documents, photos, etc. or could be from a chosen TM date.  If you should need to recover files/folders from this archive you would just copy them back to your computer (TM would not be involved).
In my view a better way to proceed is to use a cloud backup service which will maintain a daily (or more frequent) backup of your files maintaining versions of files from all times in the past in a storage efficient way - just like TM.
You should not expect a cloud backup to provide complete system restoration. Rather to recover documents, photos, etc. in the event of a disaster which might just be mistaken deletion of a single file all the way up to complete loss of your computer system and its external disks.
I suggest you explore Backblaze and Arq.
Backblaze is frequently recommended though I have reservations regarding its failure to backup some file metadata.  It provides both a backup application and cloud storage in a single plan.  It is intended to be be simple to use and by default does backups of nearly everything.
Arq (my favourite) is most commonly used as a backup application with whatever storage you choose to use - e.g. AWS, Google, etc.  I use Arq with cloud storage from both OneDrive (part of Microsoft Office subscription) and Backblaze's B2, though is unnecessary to use 2 storage providers.  Arq is similar to Time Machine in that it does scheduled backups and thins old backups to one a day and then to once a week. Compared with Backblaze it requires a little more configuration.
Please note that cloud backup does not replace the need for Time Machine (or some other local backup).