Necessity is the mother of invention
I was going to simply agree with @jdunlop but I disagree with his/her reasoning à la free time. Magic is an alternative to invention, and in old times, invention was considered to be magic for its ability to expedite tasks. Humans are a society governed by the same economy imposed on us by our nature, being a species limited to a number of years as you put it.
If society had two solutions to a given problem, such as shooting an enemy with a weapon; the one involving a great deal of time, money, and invention, such as producing a gun to fire a slug of metal at a high speed; and the other being some incantation that launches a bolt of lightning from your hand in a direction of your choice, the effort to construct a gun might simply never be put in. Why would we? Ultimately, the decision of whether to use a magical ability or a technological solution will depend on a number of factors, including the cost, reliability, and versatility of each option. However, in general, because the cost of a magical solution is effectively zero by definition, the discovery of a magical ability is likely to lead to a decrease in the pace of technological advancement in that task area.
Why do I say the cost is zero? Because in a causal universe governed by physics and laws of conservation, the cost of any activity is balanced across the almighty equality sign. Nature and her forces are defined by that single ability to make both sides balance out, such that nothing is ever created nor destroyed throughout any causal relationship. Magic, on the other hand, is a supernatural concept which ignores this balancing act. Of the various definitions available they all follow that theme.
Collins states it succinctly:
Magic: n. The power to use supernatural forces to make impossible things happen, such as making people disappear or controlling events in nature.
The key word here is super, which implies that it is outside of nature's explanations. It can't be achieved through natural events, and is thus outside the purview of science.
Since the OP asks specifically on this point, a world which could scry answers from crystal balls or divine them from a Tarot deck reliably would certainly not invest billions of dollars into developing power hungry computer chips, Internets, or artificial intelligence.
If oracles could ask their gods for answers to future events, there would simply never be any stock exchange, no investors to pour money into new electric vehicles, and no news reports of economic fluctuations. If humans could teleport, there would be no investment into security devices or doorbell cameras or cell phone tracking. What would be the point of it?
- Bob: "Hey, I have an idea! What if we could see who's at our door even when we're out shopping? I can invent a camera that uses radio waves to chop a picture into little bits, transmit them over some huge towers powered by electricity so I can put them together on a radio telephone and see the picture anywhere I am! Wouldn't that be great?"
- Sam: "You still use a door? Seriously? I just spoke to my kids at school and they reminded me, I thought we were going fishing this weekend? You going to spend all your time on that stupid workbench now?" saying this as he puts his miniature crystal ball back in his pocket.
It is not just the availability of free time that allows for technology, people will not invest their time or effort into efforts that simply do not meet any need. Since magic accomplishes impossible tasks, it removes the very need for technology in the areas it works. If your world has magical flight or levitation, they will not build airplanes unless the flight is somehow limited to very slow speeds. Likewise for teleportation. If your world has premonition, oracles, precognition, or future sight, then neither stock markets nor computers will likely ever arrive. Without stock markets most inventions will never get funding, and technology will come to a halt. If your world has magical projectiles or lightning bolt type weapons that don't need any gun-like device, then ballistic weapons won't ever be invented.
Because magic circumvents the resources required to invent technology, it is superior to technology in filling any needs for the areas that it operates. Therefore, magic will logically slow technological advances in all areas where it overlaps with technology.