Several points -
Perhaps a better model might be what is being done to recover the salt flats that used to be the Aral Sea. They built a dyke across the northern half to reduce the amount of evaporation area; the small northern part is slowly refilling and may actually be a viable fishing source in a few years or decades.
But the area suffers from the same problem as the Colorado River and Salton Sea. Decades of agricultural run-off and over-irrigation have created toxic dust that pervades the area.
A similar project to what the OP proposes is the siphon to refill the Dead Sea. they start from the advantage that - it’s already dead. More salt would not be a big deal. Running from the Gulf of Aqaba over a hump, it will also conveniently provide hydro power on the way down, but only because we’re talking 1000 feet of downward, not a few feet. For now, the Dead Sea is slowly(?) lowering at about a meter a year, because of (what else?) excessive taking of irrigation water from its primary feed. So the OP would suggest creating a giant Dead Sea in the middle of Australia.
Due to earth’s rotation, coriolis force, and prevailing weather patterns, I assume any benefit from evaporation - higher precipitation - would most likely accrue east of the lake, which is not the place that more desperately needs more precipitation. Again, would this rain actually fall on the land, or simply travel east enough to fall in the Pacific? Is there a benefit?
Other projects are as mentioned, filling the depressions south of the Mediterranean, perhaps reaping some benefits from any change in the weather. I recall a book (published in the Soviet Union in the 70’s) that described assorted projects - the most interesting was a giant dam on the Congo river, which would creat a giant lake flooding the Congo basin (can you say environmental impact boys and girls?). The dam, if high enough, could allow water to diver to refill Lake Chad and then on to the sea from there. Far too sdisruptive, though.
Another project is the Toshka Lakes. There’s a branch off lake Nasser (there thanks to the Aswan Dam) that can feed a series of lakes and possibly create a second Nile River valley, creating desperately needed new farmland in Egypt. For now, the Sudan’s massive dam project has inhibited the flow of the Nile and any such plans; The same problems exist as with other posts above - can the plan actually provide enough water flow to counter evaporation and provide a benefit without diminishing the existing Nile ecostructure?
(Recall an article about irrigation after Aswan - Egypt discovered salt buildup on farmlands when the river no longer flooded. Even fresh water has a modicum of dissolved salts. Egyptian farmers learned they had to over-irrigate regularly to flush out salts that accumulated from evaporation)