FSTs are “expensive” to re-optimize and so it’s typically done “without writes”. So the database would need some workaround for that low write throughput.

To save you the time thinking about it: The only extra parts you’re missing are what Lucene calls segments and merge operations. Those decisions obviously have some tradeoffs (in Lucene’s case the tradeoff is CRUD).

There are easily another 100 ways to be creative in these tradeoffs depending on your specific need. However, I wouldn’t be surprised if the super majority of databases’ indexing implementations are roughly similar.