The value is always zero, looks like it's completely ignored. Beside initializing it to 0 is that column never referenced at all, so it's completely missing and not simply broken.
I think we do have to extend simplenews_mail_spool(), count the sent mails per nid and not global and execute an update query for each nid.
We can the extend the existing send tests and assert the correct amount a few times in some of the existing send tests, that should be enough. maybe add a test that sends two nodes to two different categories in parallel to make sure they are both updated correctly.
Additionally, we can extend it for the content translation integration and use the actually used nid. SimplenewsSpool already has support for this, see getProcessed().
PASSED: [[SimpleTest]]: [MySQL] 1,842 pass(es).
FAILED: [[SimpleTest]]: [MySQL] 1,754 pass(es), 6 fail(s), and 12 exception(s).
PASSED: [[SimpleTest]]: [MySQL] 1,807 pass(es).
FAILED: [[SimpleTest]]: [MySQL] 1,797 pass(es), 2 fail(s), and 1 exception(s).