Are the joist repairs in my home safe and correct?
I tend to answer in practical terms, and not in strictly code-compliant or legal terms. In cases like this, code doesn't really apply since it's old work and you're making improvements. We're only talking two joists, right? That's not so terrible.

No, this repair was not done well. Short joist patches only work if they're fastened really well. These aren't.
No, your floor won't immediately collapse (unless you store grand pianos or stacks of aquariums above).
Yes, I would seek to fix the situation. Full-length sistering isn't normally too difficult. I'd do that, and take precautions such as temporary posts if you're removing lumber to fit new. The sting in your wallet will only be due to the crazy price of lumber at the moment.