A book that covers these kinds of questions is Hard sayings of the Bible, the summaries quoted below. The Bible is written in the languages and concepts that the readers would understand. Judges can be particularly difficult for use to understand in modern times. Often it seems that we don't get to a full theology of God until Isaiah.
שׁלח (send) can have the sense of allow, such as with Pharaoh in Egypt וְלֹ֥א יְשַׁלַּ֖ח אֶת־הָעָֽם׃
(and not let the people go) in Exodus 4:21,23;5:1,2;6:1,11;7:2,14,16;8:1,2,8,20,21,28,29,32... many more. There שׁלח is translated "let go." This possible meaning is also expressed the lexicons.
שָׁלַח
- send: human subj... 2. send: subj. י׳ (God) ... 3. stretch out, especially acc. hand ... 4. rarely send away ... 5. let loose
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Brown, F., Driver, S. R., & Briggs, C. A. (1977). In Enhanced Brown-Driver-Briggs Hebrew and English Lexicon (p. 1018). Clarendon Press.
9:23 God Sent an Evil Spirit?
See comment on 1 SAMUEL 16:14; 1 KINGS 22:20–22.
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Kaiser, W. C., Jr., Davids, P. H., Bruce, F. F., & Brauch, M. T. (1996). Hard sayings of the Bible (p. 193). InterVarsity.
16:14 An Evil Spirit from the Lord? ...
All this happened by the permission of God rather than as a result of his directive will, for God cannot be the author of anything evil. But the exact source of Saul’s torment cannot be determined with any degree of certitude. The Lord may well have used a messenger, or even just an annoying sense of disquietude and discontent. Yet if Saul really was a believer—and I think there are enough evidences to affirm that he was—then it is difficult to see how he could have been possessed by a demon. Whether believers can be possessed by demons, however, is still being debated by theologians.
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Kaiser, W. C., Jr., Davids, P. H., Bruce, F. F., & Brauch, M. T. (1996). Hard sayings of the Bible (p. 211-12). InterVarsity.
22:20–22 Is God the Author of Falsehood? ...
God can be described as deceiving Ahab only because the biblical writer does not discriminate between what someone does and what he permits. It is true, of course, that in 1 Kings 22 God seems to do more than permit the deception. Without saying that God does evil that good may come, we can say that God overrules the full tendencies of preexisting evil so that the evil promotes God’s eternal plan, contrary to its own tendency and goals.
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Kaiser, W. C., Jr., Davids, P. H., Bruce, F. F., & Brauch, M. T. (1996). Hard sayings of the Bible (p. 230). InterVarsity.
Here is a commentary that discusses this subject.
Ver. 23. And God sent an evil spirit. Friendship among the wicked is only a league of vice against others. In itself it cannot stand. Wickedness, says Hesiod, prepares its own punishment. Abimelech, it seems, ruled three years in peace. Plutarch, in his noble treatise on the purposes of the Deity in so often delaying the retribution due to crime, finds the ground of it in the wisdom of Providence, which knows the opportune moment for punishment. Here, as in other passages where he speaks of unholy men, our narrator names the recompensing deity Elohim, not Jehovah. Elohim sends the evil spirit of discord among them; for the undeviating law by which sin punishes itself, is grounded in the very nature of the Deity. It would be the destruction of the justice and truth of the divine government, if worthlessness escaped its recompense. The moral universe is so constituted as to ensure evil fruits to evil deeds. The experience which here presents itself is one of the most common in the history of states and individuals. It is the type of all unnatural conspiracies against right, and of their issue. It is moreover demonstrative of the perfect clearness with which the divine government of the world is apprehended in the Book of Judges, that the falling out of vice with itself, and the stopping up by wickedness of the natural sources of its own advantage, are represented as the action of an evil spirit sent by Elohim. Shechem now seeks to deal with Abimelech, as heretofore it helped him to deal with the sons of Gideon. Treason began, and treason ends, the catastrophe.
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Lange, J. P., Schaff, P., Cassel, P., & Steenstra, P. H. (2008). A commentary on the Holy Scriptures: Judges (p. 149). Logos Bible Software.