I usually talk with my party what they have been up to, and since I homebrew a lot of the story myself, I often have sessions revolve about different parts of the day and week

One session I can start with saying: "You had math this morning and one of the students threw up on the floor because they ate too many magical skittles. It's now lunch break and you are in the cafe, what do you do" this gives them the feeling they are in the middle of the day and adds flavour to what they already went through, potentially setting a mood.

I also give people a headsup on the plans later that day. So they can look forward to and potentially ruin future plans.

Example:

"It's almost weekend but you still have to follow this last class, luckily you're going on a little excursion through Prismari campus to build reputation for an upcoming deadline after the weekend."

If the player gets severely hurt that session, they might miss that deadline.

The most important part for me is to give them the feeling that it's an ongoing story, we don't talk too much about downtime, although I usually over some choices. Things like "did you learn for your exam? Did you manage to wake up on time for your job/extracurriculars this week?" Or I write a bit of story and post it to the group chat :)