Is it okay to give students advice on managing academic work? My journey through academia has been a hard-fought battle against myself and all my worst traits. I'm now finishing my PhD and concurrently teaching courses in which I inevitably come across students who do things that remind me of my own mistakes. I find myself empathizing and trying to find bits of 'life wisdom' to impart, with the goal of being helpful.
I don't remember ever being on the receiving end of such an email. I'm also certain that my colleagues don't it, which, given that they're quite good at their jobs and I'm relatively new at this, makes me want to evaluate this tendency critically.
Here's an example:

Student missed a deadline for a makeup assignment. Class policy
(decided elsewhere) is that this forfeits their right to an exam
retake. So I send all the boilerplate emails, and they apologize,
saying that they didn't have the time or energy to get it done before
the deadline.
I totally get it, so I write back that I'm sorry, I understand it's
rough to play catch-up in these situations. Then I said that teachers
often have greater leeway to offer students who ask for extensions
before it's due, and that sending a quick email to a teacher explaining the situation upfront can be really helpful. I say that I
was totally oblivious to this fact when I was a student, so I try to
tell students this now.
Then, I explained that it was still really important to complete the
replacement assignment anyway, because it's easy to glance at it,
think you understand it, then realize during the test that there were
nuances in its application that you didn't actually understand.
Then I offered to look at the student's assignment if they could send
it within a few days, just to make sure there weren't any obvious
knowledge gaps.

It seemed reasonable as I was writing it, but afterwards I wonder if it's preachy and patronizing. Given that it's exactly the sort of advice I give my teenager on the regular, it makes me wonder if it's the sort of communication best left to their parents and not their teachers.
It's totally appropriate especially for first year students. Learning college level study skills is one of the crucial tasks of the first year.  Additionally, many students whose parents did not attend college (and even some who do have such parents) are totally unaware that they can do things such as attend office hours or email the professor if they need an extension or have a problem.  In fact the way you have structured this, you could even in the future think of developing such knowledge as a learning outcome.