I have heard repeatedly that the reason God doesn't use His omnipotence to prevent people from doing evil is that He wants people to freely choose not to. This doesn't make sense to me though, because it implies that He doesn't have true omnipotence, He's limited by the definition of the term "free will". I mean, if He really is omnipotent, why doesn't He just change the definition of free will so we can have free will without being able to do evil? It seems to me like the "God wanted us to have free will" argument just kicks the can, it doesn't actually answer anything. What am I missing?
I'll answer from what I hope is a Catholic perspective. God cares a lot more about reality than about words. If He were to change the definition of "free will" and give us that newly defined sort of free will, then He could indeed say, just as He now can, "I gave you free will." But His intention is not primarily to be able to say those words; His intention is to give us the real faculty described by the old definition of "free will", regardless of what words (or perhaps no words at all) are available to name that. So, after your proposed redefinition, if God fulfills His intention in this matter, the real situation would be exactly as it is now; only the English description of it has changed. In particular, sin would still happen.
Free will and omnipotence
The question is: "God doesn't use His omnipotence to prevent people from doing evil ... He wants people to freely choose not to ... [but] it implies that He doesn't have true omnipotence"
But is this a valid understanding of omnipotence? If you have the power, which one is harder: to force people with the threat of punishment (or deny the choice completely), or to be vulnerable and self-restrict yourself from utilizing the power you have?
Therefore, God's giving us free will is consistent with his omnipotence.
Christian speculation on why God give us free will
The standard analogy is that of a father to a child, an analogy that is valid to use, since Jesus Himself used it (cf. The Lord's prayer: "Our Father who Art in Heaven", or "How much more willing your Father who is in heaven ..." Matt 7:9-11).
Compared to a 5 year old child, we are "omnipotent", but don't we as parents want our kids to obey our commandments freely? Or would you rather have robot kids who always obey (like Dreykov who modified women to become black widows in the 2021 film)? So we train our kids from toddler to childhood, through teenage period, even to young adults. We model, we reason, we appeal, we threaten, we punish, we reward, we love, hoping that in the long run they choose good more or less consistently, not evil. In other words, we parents do moral formation through spiritual formation so the child's will is more and more conformed to how Jesus obeys his Father voluntarily.
Therefore, it makes sense to see God as restraining His omnipotence and to give us a certain type of "free will" in order to obey the commandments He put in our conscience (which is part of our human nature). Even after this "free will" is damaged by the Fall, this "free will" can be restored gradually through the grace of the Holy Spirit, part of the new life we receive when we come to faith in Jesus Christ.