Hi,
I made a research on the project. I tried with the Delphi 10.3 sample project. I used several launchModes and some other activity attribs. But, I couldn't reach your objective.
What I found out is this. Firstly, Deplhi does not support second activity. Secondly and more importantly, Chrome always start a new task during sharing. But, Delphi does not suport more than one task on Android correctly. Even if launchMode is set as standard (i.e. multitasking is allowed) after second task is launched, it is put into a locked state. After first task is finished, it is unlocked and it resumes.
I think Chrome starts sharing activity with fFLAG_ACTIVITY_MULTIPLE_TASK flag and one of FLAG_ACTIVITY_NEW_DOCUMENT or FLAG_ACTIVITY_NEW_TASK flag are set. These flags causes activity to be started in a new task.
Tu sum up, the problem is related to Delphi. If you inform them, they may solve this problem by removing locking for second task.