They have not been observed. They were predicted by Dirac and many GUT models.

Dirac proposed magnetic monopoles which would simplify the model of electromagnetism. Dirac monopoles would not fit into the standard model, and would require modifications.
In GUT theories, early universe would’ve produced magnetic monopoles. But it is hard to reproduce, and LHC energies are too low for them.

Studies

Nature Materials Article (Open Access) (2014): Discovery of magnetic monopole quasi-particles in a spinor Bose-Einstein condensate. They do violate the zero-divergence law.
HN Thread | Nature Materials Article (Open Access) (Dec 2023): Discovery of magnetic monopole quasi-particles, which are multiple particles whose combined spin effects generate a monopole on a 2D cross-section. Not a big deal fundamentally. But could be in line with my idea of making magnetic monopoles manually.

Implications

Their existence would imply:

Maxwell’s equations would clean up
- $\nabla \cdot E = \frac{ρ}{ϵ _{0}}$
- $\nabla \cdot B = μ_{0} ρ_{m}$
- $\nabla \times B = μ_{0} ϵ_{0} \frac{\partial E}{\partial t} + μ_{0} J_{e}$
- $\nabla \times E = \frac{- \partial B}{\partial t} - J_{m}$
Quantization of all electric charge as proposed by Dirac
- $2 q_{e} q_{m} = nπ$
We would be able to catalyze proton decay via the Rubakov-Callan effect.
- With this, we could get energy from protons using monopoles without using up the monopole itself.
Other than that technological impact would likely be zero since they are rare.