Technologies that rely on evolution
Evolution is not the type of theory that is mainly directed towards technological applications, as opposed to many physical theories. It is a principle to understand living systems, from the simplest to the most complex. So it mainly gives understanding, not 'solutions' to particular problems. 

That being said, evolutionary principles can be applied to many 'practical' problems.

For one, all of the technologies that rely on sequence alignment and phylogenetic inference use models of substitution based on evolutionary principles, in which you have hypotheses based on the probability that some evolutionary changes occur (these changes can be at the nucleotide level or at the organismal level), and then you infer which hypotheses are the most plausible given the evolutionary and ecological context of the problem. A 'practical' side of this, for instance, would be to infer the evolutionary trajectory of the COVID-19 epidemic, or the study of the geographic spread of the virus given the sequences of the virus at different locations/time. A lot of modern molecular biology is based on a comparison of sequences.

Another 'application' is that of designing enzymes or other molecules, that have a desired function or feature. In fact, a recent Nobel prize was awarded to Frances Arnold for harnessing the power of evolution in her research on molecular design. 

Some other applications besides the ones people have mentioned in the comments above are medical applications. It is well known that cancer lineages evolve, so the principles from evolution can be used to better treat cancer progression, for instance by adjusting the evolutionary outcomes of a particular treatment (you can read a fascinating example here). In fact, the understanding of cancer itself, besides therapeutic interventions, has used evolutionary principles for some years now (see a nice example of evolutionary dynamics in metastases here). 

I also want to mention an important example from microbiology. It is a pressing issue of public health the fact that no novel antibiotics have been developed in the last few years, and that the existing ones are less and less effective given to the evolution of antibiotic resistance. What if we could make "evolution-proof" antibiotics? That's a fascinating question that some people are starting to explore, for instance by combining classical antibiotic treatments with phage therapy or molecules different than the traditional antibiotics (a cool paper here). 

Finally, I want to mention that these applications of evolutionary principles do not "rely" on evolution being "fundamentally correct". Evolution is a process for which we have a lot of evidence, so at this point (and for a long time) evolution is an uncontroversial fact to the scientific community. This is similar, for instance, to the fact that we have lots of evidence for the phenomenon of gravity; so what scientists are doing at the moment is figuring out the mechanisms by which evolutionary processes occur (just as physicists are looking for gravitons). Another addendum is that evolution seems to be an open-ended process. This means that many of the mechanisms we can find in evolution will be, to a high degree, statistical in nature, because there are just so many possibilities that we cannot account for all possible outcomes. This is a fundamental difference to many theories in, say, physics, where there are clear "solutions" to a problem (in the form of an equation, for instance). I say this because people keep coming up with examples that "disprove" evolution, but they just don't consider that evolution is a statistical process, which allows for "outliers". In fact, the outliers are quite informative for evolutionary theory, not at all undesirable (consider for instance the origins of life, or the emergence of consciousness, these are unique 'events' for which we have no mechanism to explain why did they emerge).