One device, regarding to which this howto is written, is the AVM FRITZ!Box Fon WLAN 7570. No, this is not supported by OpenWrt, and probably will never be!
Therefore if 7570 is not supported, there is a high chance that 7580 won't be supported either? Right?
No. When you look at wikidevi you see that both boxes don't have much in common. The 7570 is introduced 2009, and runs a TI UR8 SoC, while the 7580 is introduced in 2016, and runs a Lantiq VRX318.
I don't say the 7580 will be supported, but the reason the 7570 is not supported does probably not fit to the 7580.
Currently OpenWrt doesn't have support for the VRX318 chipset used in the 7580, so you don't only 'just' are missing a matching OpenWrt firmware image, but the most basic building blocks for creating one. While there are some attempts underway to work on VRX318, there is currently no way to know if or when that might become available - so if you want to use OpenWrt now, the 7580 is not a suitable option.
The boxmatrix website lists multiple SoC. Since I have a Fritz!Box 7581, which is the international version of the 7580, how can I double check which SoC or chipset I have? I haven't found this level of detail on the router website on the local network nor on the AVM website.
Yes, 7580 (lantiq VRX318) and 7581 (Broadcom BCM63138D) have nothing in common at all (and while there's some chance that the existing lantiq VRX2xx code might expanded to VRX318, there is no such hope at all for Broadcom - at least not for its VDSL modem, the FXS/ DECT (phone) functionality or WLAN).
Yes, but that doesn't imply that all additional components beyond the SOC itself (the IP cores for xDSL, FXS, DECT, WLAN) would be supported (and that answer is a firm no). For all supported BCM63xx devices it's safe to say that only the SOC and wired ethernet/ switch are generally working, WLAN only in the (rare) case of brcmfmac supported "fullmac" chipsets - nothing beyond that.