core: do not filter out write() if required in the very late stage

core: do not filter out write() if required in the very late stage

Before 12001b1bf067339db089d52e08fd0b4c6a9945df, write() is required for
if Type=exec. However, with the previous commit, now write() is also used
for sending handoff timestamp. Let's allow write() if necessary.

Fixes a regression caused by 12001b1bf067339db089d52e08fd0b4c6a9945df.
Fixes #33299.