Twitter effectively doesn't have an API any more (what they do have is prohibitively expensive for tinkering).
Mastodon has a culture that actively pushes back against many of the things people might want to build - any experiments with things like search or discovery improvements or even potentially algorithmic feeds tend to get a very hostile reaction from long-time Mastodon users.
Bluesky's API is wide open for innovation right now - and you can even connect directly to a WebSocket stream (from JavaScript running on any page) for direct firehose access, like in this demo https://firehose3d.theo.io/ discussed previously: https://news.ycombinator.com/item?id=42159786
Here's my own quick firehose demo: https://tools.simonwillison.net/bluesky-firehose - code here: https://gist.github.com/simonw/af2e50446f6dfc5cb514a7d6aadbb...