Algorithm choice depends on what you're optimising for. The discussion a few years ago was dozens of small web servers handling a large volume of password change traffic (10K/sec!) needing a cheap centralised service for verifying against "known bad" passwords. On a cloud hosting platform, the optimal solution is a blob store of sorted binary hashes with a small (~1 MB) precomputed index stored in-memory in the web server that lets you query the main store with 1 or at most 2 reads. This is an optimal "one round trip" request, and the per-server overhead at the front end is negligible.
However, that approach assumes a slowly changing list where you don't mind that there's a delay of maybe a few hours to merge in a new list. Large lists of password leaks are infrequent, so this works fine for this usecase.
A two-layer approach with a small frequently updated hash set on top of the large infrequently built sorted list is more generally applicable to a wider range of problems.
Bloom filters are probabilistic, and aren't much faster to create than a sorted list. They also require 'k' random reads to test, where k is a small constant such as 3 to 5. If the filter is large (gigabytes), then you can't efficiently load it into many front-end web servers. If you query it over the network as a blob, you need 3-5x the I/O operations. You can wrap it in an API service that holds it in-memory, but that's still much more complex than simply storing and querying a blob in S3 or Azure Storage directly.
"Clever" algorithms like min-heaps or whatever are likely not worth the trouble. My decade-old PC can sort 2 billion hashes in about 30 seconds using the Rust "Rayon" crate. There are cloud VMs available for about $2/hr that have about a terabyte of RAM that could sort any reasonable sized list (10s of billions) in a few minutes at most.
The original article mention a week of 80 vCores of SQL Hyperscale, which is about $6,000 at PayG rates!
Sure, developer time is expensive, blah blah blah, but waiting a week ain't cheap either, and these days an AI can bang out the code for a password file hashing and sorting utility in a minute or two.