Is it possible that some of the confirmed exoplanets are in fact primordial black holes? Recently astronomers discovered a black hole lying just 1000 light-years from Earth, in a triple star system (HR 6819) that can be seen with the naked eye. This discovery has increased the possibility that there are many more black holes hiding in nearby star systems.

However, we have not detected any primordial black hole with only planetary mass yet. What if some of the discovered exoplanets are actually the hypothetical primordial black holes?

A exoplanet detected through the transit method are very unlikely to be black holes due to its extremely small size not possible to produce detectable dimming. But how about the exoplanets detected through radial-velocity method? A primordial black hole with 5 Jupiter mass would have the same effect on the motion of the host star as a exoplanet with 5 Jupiter mass.
The first you need to determine if you're looking for a zebra or a unicorn.  That is, if there's a herd of horses before you, you expect to see all horses.  Maybe there's a wayward zebra in there.  Unlikely but possible, but you're not going to find a unicorn because, as far as we know, unicorns don't exist.

We know how planets form and we expect to find mostly planets where planets should be, so if primordial black holes do exist, finding one orbiting a star in a near orbit wouldn't be impossible, but it would be a zebra in a herd of horses.

That said, primordial black holes, at least those with planet-mass, are probably unicorns. People have looked for them without success and some estimates have put a size limit at below the mass of a planet.    Does that prove they don't exist?   Well, no, but they probably don't exist, not at close to planet mass anyway.  They've gotten some attention because a planet-mass black hole is a cool idea, but cool idea or not, they're probably not real.  Quantum black holes may form by additional dimensions and gravity getting stronger at very short distances, but CERN hasn't found any evidence of that, so it remains a neat mathematical explanation without a speck of evidence.

We can only detect exo-planets reasonably close to their star, either by transit or wobble.   A captured primordial black hole would probably have a more distant orbit - like planet 9 is thought to have.   A close orbit that could be detected and pass as a planet would be unusual.   If it formed within the proto-solar-system, it would likely clump matter around it, becoming part of a large planet or the central star, so it would need to be captured later, after the system cleared out and that's harder to do.  Gravitational captures that close to a star are rare.

A primordial black hole, with a planet's mass would be tiny, so, as you noted, detection by the transit method would be unlikely.   An Earth-mass black hole would be about the size of a golf-ball.   A Jupiter-mass black hole would be about 10 feet across.   Even when you factor in that the observed light-halo is about 2.6 times the size of the event horizon and beyond that, the majority of the lensing is just another 5-10 times the size of that, you're still looking at a very small object with just a feet to maybe a few hundred feet of transit.  That's probably much too small to create the kind of shading needed to recognize a planet.  You'd need stellar mass to begin to detect a transit and that would be detectable in other ways.

A theoretical planet mass black hole could create a wobble and could be detected by the wobble method, if it was close enough to the star that a few wobbles could be detected, timed and the planetary mass object confirmed, but for reasons above, we don't expect that kind of black hole to exist and if they did, one getting captured that close to a star would be an unexpected.  The odds are approaching draw a straight flush odds.  Not impossible, but very unlikely, and coming telescopes should provide better insight on this.  Maybe some surprises await us when the next round of telescopes start getting images, but I would guess that planet mass black holes won't be one of them.