I believe it is fully synchronized, I've been running it for a few days. I've tried connecting via port 50001 with no luck.
I'm not running it using systemd; I start it manually. It writes logs to the console, which presumably is the same I'd get with journalctl.
When I start it, the last few lines look like this:
[2023-07-27T20:09:22.850Z DEBUG electrs::p2p] got 4 new headers
[2023-07-27T20:09:22.850Z INFO electrs::index] indexing 4 blocks: [800522..800525]
[2023-07-27T20:09:22.850Z DEBUG electrs::p2p] loading 4 blocks
[2023-07-27T20:09:25.698Z DEBUG electrs::index] writing 29471 funding and 32801 spending rows from 10260 transactions, 4 blocks
[2023-07-27T20:09:25.868Z INFO electrs::chain] chain updated: tip=00000000000000000000a1a96c9dc4b97842999d39edaeb0e1629066dc38be91, height=800525
[2023-07-27T20:09:28.986Z DEBUG electrs::p2p] got 0 new headers
[2023-07-27T20:09:29.438Z INFO electrs::db] starting config compaction
[2023-07-27T20:09:29.456Z INFO electrs::db] starting headers compaction
[2023-07-27T20:09:36.079Z INFO electrs::db] starting txid compaction
and then nothing more is logged until I try to connect.