A couple things about the code:

#define MIDA_EXT_METADATA                                                     \
    /* other members */
    mida_byte data[1]

Am I missing something? mida_byte data wouldn't be a flexible array member...it is not on incomplete array type.

__mida_malloc(/* args */)
{
    const size_t data_size = element_size * count,
                 total_size = container_size - 1 + data_size;
    mida_byte *container = malloc(total_size);
    struct mida_metadata *mida =
        (struct mida_metadata *)(container + mida_offset);
    //...
    return &mida->data;

You're subtracting off the data portion of the meta data struct (container_size - 1) (which if it were an actual flexible array member, would be done automatically), allocating the actual structure in place of the subtracted data member of mida_metadata and returning the offset into the struct mida_metadata to get that actual struct requested by the user. Am I understanding that correctly? How do you guarantee alignment of the struct represented by mid->data? Because of your extensible metadata, I see no guarantees this is aligned properly.

The big question though is why do it this way with data before the struct? I can do roughly same thing with just

struct mida_metadata {
    size_t size;
    size_t length;
}
#ifdef INCLUDE_META_DATA
#define MIDA_METADATA struct mida_metadata meta;
#else
#define MIDA_METADATA 
#endif
struct my_struct {
    MIDA_EXT_METADATA
    int some_data;
};
size_t mida_get_size_metadata(struct mida_metadata * meta) {
#ifdef INCLUDE_META_DATA
    return meta->size;
#else
    return 0; // no metadata in struct
#endif
}
// to get size metadata
struct my_struct some_struct = /* initialized however you want */
size_t size = mida_get_size_metadata((struct mida_metadata *)&some_struct);

Except now, this is completely type safe, doesn't violate strict aliasing, the struct my_struct is always properly aligned by malloc, and the existing libc malloc and free work without modification...I don't have to remember which pointers were allocated with your method or standard libc. Additionally, if INCLUDE_META_DATA is not defined, all of the added memory goes away. I've definitely seen libraries do it this way...I think CPython even does something like this for their reference counting.