Online backup strategy or software for computer and external drive
I'm not sure there is a way to do this exactly how you wish it, but perhaps some things to consider…

I'm not sure Backblaze or anything similar is capable of 'knowing' that files moved to a different drive are still the same files - however, the remote servers will hang onto the old copies for 30 days after they are last seen, which should be plenty of time for the new copies to make their way to the backup.

From personal experience, Backblaze shifts around 20 - 25GB of data every day from my machine, so a few GB of photos every month wouldn't be much overhead on that.

One thing I do, as belt &amp; braces, is I have a local Time Machine backup too, to cover for most disaster recovery scenarios, short of the house burning down.

One other thing to consider is that the initial backup may take quite some time - mine took 3 months running 24/7 on a 12Mb UL line! (My total off-site storage at Backblaze is around 2TB.)
During that time you are not completely covered, which makes the Time Machine even more important.