Are you using the new Image Backup Format or the legacy format? In order to keep different versioning between cloud and local, you'll either need to use the legacy format and select different Retention policies for each:
1 - Cloud: Keep Number of Version to 1
2 - Local: Keep number of versions as needed
3 - Schedule: Recurring Advanced. Run the Full backup as needed. Run Block-Level Incremental in-between full backups.

The limitation here is that you cannot use Synthetic Full Backups as they are not supported for local backups, so every full image backup will have to run in it's entirety.

The better option is to use the New Backup Format which has better performance and built-in integrity and restore verification (if needed). You would create different backup plans for local and cloud (Hybrid Plans are not yet). For the cloud backup, we use synthetic fulls. You can schedule the Full to run something like once a month and incrementals daily. If you set retention to keep backups for 1 day, then the old backups will be removed when the new full is created (meaning, you'd have a full plus a month of incremental backups in storage, then the next full is created and the previous backup set would be removed at that time). If you set retention to keep backups for 1 month, then the previous backup set would not be removed until the send month was complete, meaning, you'd have 2 full months in storage for a while.

Can I ask in what region you are located? If cloud costs are a concern, there are low-cost cloud storage options that might work for you (depending on where you are located).

David/MHC - A couple of points:
1. Wasabi has a 90 day timed-storage policy, meaning that if you purge data prior to 90 days, you still get charged for 90 days. BackBlaze has no such timed-storage restrictions.
2. I am working with support to understand why the retention/purge process behaves differently with the New backup format (NBF) compared to the old format.
Simply put, in the old format I could run a weekly full image backup to BackBlaze with a 3 day retention period, and when the next weekly full ran, the previous week's image would get purged (as it is over three days old). I end up with one full image.
That is NOT what is happening in NBF.
Using weekly Synthetic Fulls only - no scheduled incrementals, with the same 3 day retention period, the previous week's generation is NOT getting purged at the completion of the the new synthetic full.
I am in the process of trying the one day retention setting to see if it changes the behavior, but for the life of me I do not understand why it doesn't work the way it used to. Once the synthetic full completes there is ZERO dependency on the prior generation.

If you use our Unified Billing Powered by Wasabi, we only require a 30 Day retention. But you're assessment is correct: If you keep data for a single backup and you have a retention requirement on your backup storage, then you're likely going to pay for more than 1 backup. Depending on your region, you could use Backblaze B2.

I'm in Belgium and I use Wasabi, the cost are satisfying for me.

I just configured the backup as you say, I will check later if this is ok.

Thanks !

Please keep in mind what Steve said. If you have a 90 day retention requirement with Wasabi with your account, then deleting backups way before the 90 days' is up, leaves you with fewer backups and no reduction in backup storage costs since you'll be charged an early deletion fee. At that point, unless you have a reason you do not want to keep those older backups around, you might be happier keeping a months' worth of backups so you have more restore points available for restores. Just something to consider.