The bacterial 'homing missiles' that scientists want to harness

The shows in question generally a) hire specific writers for this, and b) don't really give that much care to this. Even Trek, which had a manual that detailed the fictional systems in depth (The TNG Technical Manual was a writer's guide written by the artistic directors), let it slide for the point of the plot.

And ultimately, these snippets are just filler that add background to the world in question. To people who aren't you, or me, they do not matter all that much.

There's 'Autonomous' by Annalee Newitz which has lots of things like that https://www.goodreads.com/book/show/28209634-autonomous

I recommend https://en.wikipedia.org/wiki/Cells_at_Work!

"The story takes place inside the human body, where trillions of anthropomorphic cells each do their job to keep the body healthy. The series largely focuses on two such cells; a rookie red blood cell, AE3803, who often gets lost during deliveries, and a relentless white blood cell, U-1146, who fights against any germs that invade the body."

For a never-ending rabbit hole: https://tvtropes.org/pmwiki/pmwiki.php/Main/BiologyTropes

Literally was just thinking the same thing. Maybe if you put a export tag on it so the cell secreted it, but you'd probably run into glycosylation differences (since these are bacterial proteins naturally) and you'd probably make very little, again because it's a bacterial protein and not one normally made in mammalian cells (like SARS-CoV-2 spike). The approach I would take (just thinking aloud) would be to solve the structure of the tailocin (probably easy by cryoEM since it's highly structured) and work out the business end mechanism then iterate humanizing it while keeping the important bits constant. I guess it boils down to "probably not straight-forward".

Is that not by definition a self reproducing virus ?

Probably it would have a vaccine effect, so the human immune system would then fight the phage which is the opposite of what you want...

Using a "live" phage also has the advantage that it would coevolve with the pathogen, the mRNA produced tailocin is always the same and the pathogens would probably become resistant quickly.