I *think* they are all compatible. The flex edge beater for the US market says it's compatible with the 7990 and 7581. I am assuming the 7580 and 7581 are compatible. This non-official website shows attachments fitting both your 7580 and 7990, as well as 7581:
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If so, then this is further evidence of compatibility, because parts from Kitchenaid Australia and USA Kitchenaid have identical part numbers, and fit 7581 and 7990:
Fits "6.9L Bowl Lift Mixer models KSM7581, KSM7590 & 7.6L Commercial Mixer KSMC895"
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Having said all that, just make sure that you actually have a 6.9 L machine: this Amazon ad has the 5KSM7580 as being a tilt-head mixer:
https://www.amazon.com/KitohonAld-Compatible-Kitchenaid-Artisan-5KSM7580/dp/B09TXLXHJB
But this eBay ad has it as a bowl-lift:
https://www.ebay.com/itm/254091789859
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Let us know what you find out if you order something; I've obviously spent a lot of time trying to figure out what things are compatible without much luck, on a similar situation on my own machine.