Let me share my workaround as well. It is based on a few solution I have read here already, but I tried to be more precise about what needs to be done.
1. Load a save game, that doesnt trigger call right away - I have multiple saves that start call right after I spawn in the game. They are useless for this workaround. You need a save that will start call from Takemura after you will do a few steps
2. Call Judy - ok, so you have loaded a game and you know you will get a call from Takemura after you move a bit. Dont move and call Judy
3. Keep call with Judy active and go to the closest unknow quest that is marked with yellow ? - no need to interact with Judy during the call, just keep it active. Now open map and find closest unknow quest with yellow ? mark. The point is to find a new quest from Regina Jones. Go to the ? mark
4. If the uknown quest updates and you get SMS from Regina Jones, move around a bit and hang up call with Judy - In my experience there are plenty of quests/tasks from Regina so you should not have hard time to find one. What should happen is that when you get close to unknown ? mark, quest should update and you should get SMS from Regina. Now remember, you are still in a call with Judy. After you get SMS from Regina, move a bit for a few seconds and hang up call with Judy
5. After you hang up Judy call, you should get call from Regina as well as Takemura at the same time. Reginas call will be priority and after she will hang up, she will cancel Takemura as well
6. Play the game a bit and you should get another call from Takemura, but this one will be working as intended and will update Takemuras quest
Hopefully this will help you. To sum it up, load the game, call Judy right away, with active Judys call move around the map, find a new quest from Regina and after you get SMS from Regina hang up Judys call - you should get call from Takemura and Regina right away and after you finish this call you will no longer be stucked on call screen. If Regina wont call you after she sends you SMS and you will hang up Judy, repeat 1,2,3 and try to find another Reginas quest/task