Both happen! It's just work on phage therapy had to reinvent itself in the last decade or so and modern techniques are only just reaching maturity. We're gonna see a lot more development in this space over the next decade.

I have not kept up on antibiotic resistance research, or phages in recent years.

I do recall a number of years ago, I believe in the US, someone scooping up pond and garden soil samples looking for new phages.

A quick search though, does show work on "phagemids"; the following article does mention that phages can cause harm to the human host by releasing harmful toxins in the bacteria when cell lysis is performed (potentially causing sepsis, or death), as well as bacteria do also develop resistance to phages over time.

https://news.mit.edu/2015/engineered-particles-kill-harmful-bacteria-0625

I think bacteriophages should be investigated much more, unfortunately I don't think big pharma is that interested in them, although they are also pretty uninterested in antibiotics too, because they generally don't make much profit. So I think at least in this economic model in the west we are unlikely to have them widely available. I am admittedly quite out of date, all I remember is that there was more research and use of them in eastern europe/russia.

resistance genes are often carried on transferable elements like transposons and plasmids, which often contain multi-gene cassettes encoding for many types of resistance. I would also like to be hopeful too, but every antibiotic we have developed has had resistance develop against it, also within multidrug resistant strains like MRSA and CRAB. I think we should be hopeful for phage therapy, as well as AB + phage combination therapy. I think relying purely on antibiotics is a bit of a dead end.