For the self-employed, when you confirm eligility online, you are asked when do you expect to return to work, with options of within 3 months, within 6 months, or not sure. This would suggest that extension is at least being considered.
Seems like a GDPR issue to me. There must be some lawful basis for the information sharing. I'm not aware of any rule that would allow sharing in these circumstances. Would have been very easy for them to seek consent when confirming the payments, but they don't seem to have done that.