Not really. You could do it the way the Have I Been Pwned database works.
You hash your query and then send only the first X number of bits.
The server returns all results that hash up to that same first X number of bits.
The server doesn’t know exactly what number you were looking for, and you don’t have to download the entire database.
But in this case the server WOULD be able to figure out the set of possible phone numbers you were asking about. Because of the complexity of passwords the search space would be a lot larger.
So privacy wise this does seem better.