I logged into my account and downloaded the update, and I was brought to the "Quick Play Screen" , I logged out and restarted and was able to play on any toon, i logged back out and back in and was greeted by the "Quick Play Screen". I have not switched how I down load updates as was previously recommended. I have multiple accounts,I do play with my children and I can not switch between them unless I restart my personal pc after logging out from the active account.

I've been having this issue as well since patch day and found that if I stop and exit the game and attempt to initiate a new session that I get the stuck on character select screen. I found out that I had to restart my PC as my daughter had logged into her account from my PC and was able to access all her toons but when I logged into my account on the same PC I could not. If I recall correctly, wasn't this an issue that popped up with the cache not clearing some years ago? I recall it too happened after a patch and was causing problems and Bioware had to do an emergency patch for the cache to be cleared during the log in start up sequence. Hope this helps as a memory jogger for the devs.