This has been my experience too. Instead of going the logical replication route I tend to leverage the transactional outbox to achieve consistency in the application layer instead.

So when I transact data into tables I immediately fetch the latest outbox id.

And then when query from Elasticsearch I first fetch what the last outbox id of the processed data is.

This way I know if the transaction was already processed into Elasticsearch or not. Repeat. Until outbox id of Elasticsearch is equal or higher than the outbox id of the mutation.

This way I don't have to use logical replication, no k/v store and I can just use a script that fetches and processes the latest outbox changes on a loop.