I just bought the Supermicro X13SAE-F for my new Unraid build. I haven't bought the CPU yet, but looking at i7-12700, i7-12700K or i5-13600K.
I connected the motherboard to the power supply CPU 24 pin and 8 pin connectors, no CPU or RAM and the BMC works and gets an IP address from my home router.
Pointed my browser to that IP address and logged into the IPMI. There I could see the board had BIOS version 1.0b so won't work with 13'th gen.
It is possible to update the BIOS without a CPU via the IPMI, but you need to purchase a Supermicro Out of Band (OOB) Software License Key (SFT-OOB-LIC):
https://store.supermicro.com/out-of-band-sft-oob-lic.html
The motherboard selection on that order page does not show X13SAE-F in the drop down list. I used the online chat to ask and the agent got back to me and said to select X12SAE-5 for ordering the license and it would work.
I have found Supermicro support very good answering questions.
I live in Canada and could not find the Gigabyte board anywhere.
Add: I found I must have a US billing address to purchase from Supermicro directly.