Ujm,
Jews from all the groups you mentioned have taken on superficial racial characteristics of the countries that they lived. Ashkenazi Jews are lighter-skinned than Jews from Sepharad, who are lighter-skinned than Jews from Morroco, who are lighter-skinned than Jews from Yemen. Indeed, there are Teimani Jews with skin just as dark as Ethiopian Jews.
The DNA argument, even if you give it halachic credit, is tenuous at best. They don’t say that Ethiopian Jews don’t have Middle Eastern DNA, they say that they don’t have any more ME DNA than the surrounding population. But a lot of the surrounding population claims descent from Jews as well (they just converted to Christianity) and we don’t know what percentage of the original Beta Israel population was born Jews and what percentage were converts.
The Ethiopian Jews went through tremendous persecution over the millenia. The Church did not let have books other than the OT and (IIRC) they were not permitted to be written in Hebrew. It is for this reason that they lost 95% of their Torah shel bal peh. But they were not Karaites. They had some Oral Law and kept traditions (like muktzah and harchakos) that were not kept by Karaites.
The Beta Israel community sacrificed for thousands of years to keep their connection to Judaism in an extremely hostile environment. Thousands, maybe millions, died al kiddush Hashem. It seems very unlikely to me that they would have had the fortitude and hashgacha to withstand such pressures if they were not genuinely Jewish klapi shmayim galia.