Economy and market
Lets say there is company A and Company B. Company A has a magic academy/School it is funding, and raises an army of skillfull mages in variety of fields. Then, rents their services to different industries and places for fixing pretty much any problem.
Lets say, Company B has large amounts of mines, materials, lands, and engineers. Now, Company B cannot race Company A in terms of flexibility or range of applications. So, how can they race?
Reduce the cost. How? Better technology, more efficient solutions, using more durable materials, mass production.
A race in economics can bea factor for developping plenty of different ideas. And in a world of magic and machinery, when the two race against each other, people will try to get creative.
"Oh! He can throw lightning! Cool! My machine can also throw lightning! But it doesn't need to eat or sleep! So I can give you 20% discount! How about it?"
Mages takes maybe decades to raise and train. But if you kill the mage, it is teh end of mage's usefulness. But a machine? Replace the broken parts and it is ready to go... Mostly.
War, famine or other disasters causing mass deaths will eventually create scarcity on workers, or in this context, mages. But a machine doesn't need to eat. It can be fixed with a detailed user manual and people with little training. A machine can be more easily produced, deployed and maintained than a mage.
When there is scarcity and disasters, people have to get creative and efficient. Or they will die.
Extremist beliefs and traumas
"Magic is evil! But we do need light, cleaning our house, tending the field and making food. But people get wounded or die. So we need a better solution. Any ideas?"
People following extreme beliefs in different perspectives will focus on ideas and methods they feel comfortable with. Even in our world, many people don't trust modern medical science and try to seek cure from alternative methods. Makes sense? Debatable. But in a world of magic, you will have options.
For example, in modern world, you won't see many zeppelins because.. Hindenburg accident. It was a tragic accident which changed the focus on aero-engineering. A similar disaster relating magic, could do the same for a few local areas.
Generational traumas, extreme accidents, disasters... These kinds of thigns will scare people and sometimes leave generational memories preventing them to pursue those. Similar stuff could create regions and groups all focus on either magic, or machine but definetely not both. Now, people needs food, medicine, transportation... So you have to develop something.
Specialization, long-term requirements, reaching the peak.
If you consider magic like art, there will always be people trying to hone it to perfection. Trying to add their techniques. THere are art schools, art majors. People will use different methods to express themselves and luckly, magic is extremely versatile.
Also, maybe machines cannot create enough fire power or output when a mage can. Maybe only a true mage can reach to pinnacle of power. But a machine will break down after a level. Humans on the other hand, they heal. they adapt. And they can gain experience.
Machines on the other hand, has a really special place in mass production where they can beat mages in everyday use, repeated tasks and endurance on continuing a certain duty. Machines can be specialized in certain fields to fix a specific solution which could be tricky or annoying for mages. So, requirements may create different development paths for these two areas.