Naturally, you should break down tasks until you get max one day chunks. But estimation errors are common, so if you end up spending 2+ days on a "half-day task", then you should be able to explain why. GitHub/GitLab/JIRA/Phabricator/Gerrit/GoogleDocs/whatever comments, emails, commit messages, CI runs, are all manifestations of progress.
Task completion is a manifestation of time and effort, not progress. While breaking down user stories into daily tasks can be a useful crutch for newer teams that lack proper agile process discipline, highly productive agile teams find that administrative overhead to be a waste of time. In general incompetent managers tend to fall into the trap of looking at meaningless metrics just because they're easy to calculate rather than focusing on what really matters: sustained customer value delivery.
I don't really know what else to tell you, because you seem to insist on some magic definition of progress.
I work with people I trust. Their competence, ability, and integrity. If I see them spending time on tasks, exerting effort on whatever problem at hand they are solving, I'm very much certain that's progress measurable in direct customer satisfaction/value.
