[Help] PS4 Hard Drive Swap

Hey, guys. Sorry if this is the wrong subreddit.

I moved in with my boyfriend last month, and since he has a PS4, I decided to keep my old one at home for my dad and sister to keep playing on. However, I replaced the hard drive in mine with a 1TB one, and I have a lot of digital games on it, so I took my hard drive along with it (my dad gets free ones at work, so he could easily procure another). My boyfriend was down for replacing the original PS4 hard drive he had in his, with mine, since I still had lots of space for his few games on it, and he transferred all his saves to the cloud in preparation for this.

Yesterday, I took his hard drive out of the PS4, put it away, and replaced it with my hard drive. The PS4 said I needed to reinstall the OS using a thumb drive. No problemo, grabbed mine and took care of it, and then, the PS4 tells me it needs to reinitialize the system, and wipe all users and data. I declined, so my hard drive is still intact.

I now realize this is my stupid mistake, but I backed up nothing on a separate drive, and my PS+ membership expired months ago, so all of my cloud saves are way out of date. My dad already put a new hard drive in my old PS4, though he does have PS+, so he could back up his saves without issue. However, my concern is this: if I pop my hard drive into my old PS4, won't the same thing happen?

Basically, my question is, how screwed am I? Is there any way to backup the saves on my hard drive, in a way that the PS4 could read them, or am I flat out of luck?

Any help would be appreciated. I will cross-post on the forums, as well.

Thanks in advance!