How big is the .BIN file? What are you storing in it contributing to the size? Perhaps review .MAP file, or inspect .ELF with objdump/objcopy type tools. The .ELF is going to be mostly meta-data, so symbols, debug, etc stuff that doesn't live in the MCU's memory space.
You can attach external FLASH via SPI, you'll need to interact per commands in the data, and with HAL_SPI_TransmitReceive() type methods. You'd have to fetch content in to RAM for use, so managing the placement of content or a file system would likely be required.
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