Archival style backup software or online service I have some folders that I need constantly backed up.

I need to have the backup in archival mode where nothing is ever deleted. That is, new files are backed up, backed up files are never deleted, and updated files don't replace backed up files.

The folders contain financial records which need to always be kept.

I've tried Google Drive with the backup app, however, this keeps it in sync.

I've tried Time Machine, however, old files are deleted once the drive is full.

I need something like Google Vault. Where once files are added, they are retained forever. I don't use Google Vault as it requires a Google Suite account and i'm just on a personal Google account.

Can you recommend a software that can do this? Or a online service is fine as well.
I believe you can do this with Time Machine. You could set Time Machine to do a backup hourly or daily. Then tell time machine to only backup the specific folders with the data you want to backup. Time machine saves all backups until the drive you are saving to is full. The backups should be very small so a disk will hold a lot of daily backups. You can monitor the remaining free space on your destination drive and get a new disk when the one you are using is almost full. 

The real trick could be restoring a backup. I think restoring may replace current data. You could test this out using hourly backups to see how it works. After a couple of hours, try to restore and see what happens.

There is a 3rd party free app called TimeMachineEditor that will enable you to change the backup interval from every hour to different intervals in hours, days or weeks.