Selfhosted

This might be a little overkill, but Home Assistant can do this.

1. Add the calendar to Home Assistant. You don't have to manage it there, but it'll have access.
2. Under Settings - > Devices & services -> Helpers add a helper of the type History Stats.
3. For the Entity, select the calendar you want to track, and the Type would be Time.
4. Next it'll ask you which State to track. Depending on the specifics, you'll probably want to track if the calendar is On, meaning there's something on the calendar. You can track multiple States, but you probably only need On.
5. On the last page of the wizard you'll put start and end times. If you want to track from Midnight until Now, here's what it would look like:

Start: {{ now().replace(hour=0, minute=0, second=0) }}
End: {{ now() }}

You can probably adjust the end time to 23:59 if you want to see what's in store for the day looking ahead, but I haven't tried it.

I searched around a bit and found https://github.com/dreiekk/calcdav

not sure if it still works, last commit was 3 years ago (on the other hand, there was no AI vibecoding back then, so thats a plus), but it looks like it might do exactly what you're looking for

sum the time used per day

Once when I was young, I have tried this, too. It turned out that all days used 24 hours, more or less exactly. After a while I found it too boring and let it be...

/s

Not exactly that but Cfait (which I develop) is a CalDAV task manager (which has an option to create calendar events). I added a time tracking feature so you can add / manage sessions (which show up in the calendar if you chose to activate it) and you do get a total time.

https://timewarrior.net/

Not CalDav but timewarrior does exactly what you describe.

Well, you have already written the prompt 🪄