Doesn't this sort of bypass the whole point of encryption in the first place?

No, homomorphic encryption allows a 3rd party to perform operations on encrypted data without decrypting it. The resulting answer is in encrypted form and can only be decrypted by whoever has the key.

Extremely oversimplified example:

Say you have a service that converts dollar amounts to euros using the latest exchange rate. You send the amount in dollars, it multiplies by the exchange rate and then returns the euro amount.

Now, let’s assume the clients of this service do not want to disclose the amounts they are converting. What they could do is pick a large random number and multiply the amount by this number. The conversion service multiplies this by the exchange rate and returns the ridiculously large number back. Then you divide thet number by the random number you picked and you have converted dollars to euros without the service ever knowing the actual amount.

Of course the reality is much more complicated than that but the idea is the same: you can perform operations on data in its encrypted form and now know what the data is nor the decrypted result of the operation.

So homomorphic encryption means the server can compute on the data without actually knowing what's in it. It's counter-intuitive but better not think about it as encryption/decryption/encryption precisely because the data is NOT decrypted on the server. It's sent there, computed on, then a result is sent back.

I'm not pretending to understand how homomorphic encryption works or how it fits into this system, but here's something from the article.

With some server optimization metadata and the help of Apple's private nearest neighbor search (PNNS), the relevant Apple server shard receives a homomorphically-encrypted embedding from the device, and performs the aforementioned encrypted computations on that data to find a landmark match from a database and return the result to the client device without providing identifying information to Apple nor its OHTTP partner Cloudflare.

There's a more technical write up here. It appears the final match is happening on device, not on the server.

The client decrypts the reply to its PNNS query, which may contain multiple candidate landmarks. A specialized, lightweight on-device reranking model then predicts the best candidate by using high-level multimodal feature descriptors, including visual similarity scores; locally stored geo-signals; popularity; and index coverage of landmarks (to debias candidate overweighting). When the model has identified the match, the photo’s local metadata is updated with the landmark label, and the user can easily find the photo when searching their device for the landmark’s name.

Maybe they "encrypt" it in jpg? XD