After downloading new/updated resources, while Logos was still indexing, I switched back to the floating Library window and clicked on the Last Updated field to sort by that column. Then I sat and waited.
It was taking such a long time that I went downstairs and had something to eat and came back up a few minutes later. It was still doing the spinning "busy" thing where the app is not responsive.
I finally couldn't stand the wait and switched away (Alt+Tab) to start typing this bug report, then switched back and it had finished sorting (though indexing was still in progress). I closed Logos almost immediately after this.
Log attached. (I waited until after Indexing finished to attach LogosIndexer.log.)
0310.Logos.log
6545.LogosIndexer.log
I am pretty sure the moment I activated my Library before clicking to sort by Last Updated was 00:24:51.2096 in the above logos.log file. After that point there are a lot of SQLite lines that seem to take more than 10 or more than 20 or even more than 30 seconds. I'm attributing the waiting around I had to do to how long all these things were taking.
So from starting to sort until it finally finished and I shut down Logos was about 8 minutes. (I suspect it would have gone on longer if I hadn't Alt+Tabbed away and back.)