This was probably not the case long time ago when the question was asked, but nowadays there are different backup utilities that support this either directly as an option or through simple scripting/additional settings.
One of the the terms being widely used to refer to this functionality is "append-only backups".
Borg backup has this functionality as a built-in option.
Restic can be set up to talk to a remote filesystem which does not support delete operations or to
rclone server which will serve any backend supported by rclone to restic, with the rclone built-in option to serve in append-only style.
Additionally when backing up to a cloud, many cloud providers (AWS, B2, Wasabi etc...) support having buckets which do not allow deleting of data or indirectly through having eternal history for all files, effectively not supporting deleting them (this setting is sometimes set up per access key, not per bucket itself).
(Update: Someone edited away links to what they called "newely created products". Note that none of those products are new, they are very well established, and some of the biggest products in the backup sphere. I have no affiliation with those products and they are all free and open source. They are about as new as rsync or duplicity (exaggeration to illustrate a point). The question specifically looked for ways to implement this, and links to specific solutions (as opposed to generic "some software probably has this function") are warranted here. In fact, I came to this question also looking for specific solutions.