Unfortunately past that point I'm entirely spitballing.

I know that tasker should be able to set and delete alarms through some built in functionality it has to interface with Android "stuff". I think it should also be able to do web requests? It has a fairly complex scripting language for custom automations once you get past what you can do with the low/no code stuff it has, and it at least used to have a pretty strong community sharing their stuff.

In theory, I'd try to see if Tasker could query calendar events directly from your calendar app. If that can't be done next I'd see if your davx server exposes an API to query info about calendar events (use that to get the start time of the earliest event), and backup for that would be to see if you could automate downloading say the next day's events as a file and get the earliest timed one by parsing that file (deleting the file when done).

Sorry, not meaning to send you on a wild goose chase or anything. I'm deep in the realm of investigating what might be possible to script/automate for work, so that's where my mind is at.