The ‘correct form’ for the stand up is tricky, and probably varies on team size. For a small team (e.g. 4 devs) you probably care a lot about what the others are doing as you’ll likely be interacting with it closely (reviewing it, building on it), sometimes larger teams (e.g. 7 devs) then it might never come your way.
I’ve found that people who stick to the classic “what I did yesterday, what I’m doing today, what blockers are there” set tend to provide really short ‘bland’ updates e.g. “I was working on task foo, I’ll be doing more on foo today and possibly starting work on bar, I don’t have any blockers”. If you’re not paying attention you can miss the fact that the same update has been reported for 3 days in a row and actually there is some unexpected complexity and/or a simpler solution has been missed.
For me, the best stand ups give a little more information and can be a trigger for a follow up chat after the standup. “Yesterday I was working on task foo, today I’ll be doing a bit more because I found doing XXX is a little trickier than expected - but I’m still hoping to get onto bar, no blockers - unless my idea for XXX doesn’t work”
I’ve also found this sort of issue made worse on projects where the Project Management have decided that we shall be “Agile” and do scrum. You then end up with a non-technical PM acting as the scrum master and mandated “best practice”. This always stifles any technical discussion as it is ‘noise’ to them, despite being ‘signal’ for technical folk....