I am looking for a meaningful explanation to Numbers 23:19. What is the significance of God being compared to a "(ish) MAN that lies" and a "(ben adam) SON OF man that relents?"
Rav Hirsch explains that an oracle speaks in parables and and can use terms that can be misinterpreted or have multiple meanings. For example the story of King Midas and the Oracle at Delphi in which the message was A mighty kingdom will be destroyed and King Midas thought he would win while he was actually soundly defeated. Hashem explicitly stated that Bnai Yisrael would be blessed and Bil'am was forbidden to curse them.
As Rav Hirsch explains
לא איש וגו. Immediately on your first request Hashem told me regarding this people כי ברוך הוא that it was blessed. Hashem does not speak in the ambiguous words of the oracles. If Hashem says that something is blessed it it is blessed, and there is not phase of it that is accessible to the reverse. And if Hashem has once said לא תאור את העם ("thou shalt not curse the people") He does not afterwards change His mind and give permission for the opposite.
Though Balak was told numerous times by Balaam that he can only state/say what The Creator instructed him to say, Balak kept insisting that they (Balaam and all the people that were with them) should go to another location and see the Israelites from a different angle as maybe that would reverse the blessings to curse. Balak got word that The Creator is not like a man who deceives, lies, and has ulterior motives or mankind who changes and wavers. What The Creator does is final and doesn't second guess himself because he is all-knowing (Isiah 55:8).