This is a known issue, but when starting the game (Steam version) the loading anchor briefly appears, goes away and then the game is stuck at the splash screen with "Synchronizing" displayed.
Deleting the preferences.xml file in will fix this issue, but it's kind of annoying doing it every time before starting the game. Just reporting to raise awareness.
I have already tried to "Check file integrity" and repair files using properties in Steam and it does not fix the issue.
update: apparently deleting the preferences.xml file does not fix the issue now, it worked for me yesterday. Also this was in the debug log but probably just from deleting the xml file
[1126/024825.955:ERROR:settings.cc(325)] Settings version is not 1
[1126/035208.205:ERROR:settings.cc(325)] Settings version is not 1
[1127/173152.227:ERROR:settings.cc(325)] Settings version is not 1
[1127/202314.527:ERROR:settings.cc(325)] Settings version is not 1
update 2: after multiple unsuccessful attempts deleting the preferences.xml file (in SteamLibrary > steamapps > common > World of Warships) I was able to log in successfully by deleting the preferences.xml file and then rebooting my computer.