Hey there,
Given that you are seeing issues not only in game but with the Blizzard Desktop application as well, indicates this is likely some sort of connection issue to the service.
The trace route shows some evidence of instability but nothing conclusive given the test limitations. We may be able to get a better look at the connection routing if you were to run a WinMTR instead.
Ideally we’d want 2 tests, each about 10 minutes long. (If you are able to get in game.) The first test while in game and seeing the high latency, the second while on the other server and seeing normal latency.
If you still cannot log into battle.net itself, then a single 10 minute test to the patch service (listed in the article) would have to do for now.