Kakute H7 Mini ships with Betaflight Firmware.
Betaflight Target: KAKUTEH7MINI
INAV Target: KAKUTEH7MINI

Ardupilot

v1.2 & prior: KakuteH7Mini
v1.3: KakuteH7Mini-Nand
v1.5: KakuteH7Mini (Supported in master/latest FW or 4.6.0 & later)

PX4

Firmware can be built using make holybro_kakuteh7mini
KakuteH7 Mini v1.5 is supported in PX4 main or version later than 1.15.4
PX4 Bootloader HEX file for Kakute H7 Mini v1.3 and before:

115KB
holybro_kakuteh7mini_bootloader.hex

PX4 Bootloader HEX file for Kakute H7 Mini v1.5 and later:(Must use QGC Daily, or v4.4.4 or later)

115KB
holybro_kakuteh7mini_bootloader_ID_1058.hex