You can add to Ambitus without opening it: by asking Siri, or from your Apple Watch. Everything goes into today's quick note.

Say "Hey Siri, Capture in Ambitus" and choose Write, Speak or Recording, as on Apple Watch. What you write, say or record is added to today's quick note, and Ambitus stays closed.
This needs the ready-made shortcut. Add it once:
To have it on your iPad and Mac too, turn on iCloud Sync for Shortcuts on each device.
On Apple Watch, "Hey Siri, Capture in Ambitus" gives the same menu.
For one quick line without the menu, say "Hey Siri, Ambitus capture". Siri asks What's the note?, and what you say is added straight away. This one works on the iPhone only, not on Apple Watch.
They go into a folder called Quick Notes, one note a day, named QuickNote with the date. Each thing you say becomes a new line that starts with its time.

The same command is in the Shortcuts app, under Ambitus, as Add Quick Note. You can type the note there, or put it on your Home Screen.
If Ambitus isn't on your watch:
After that, it updates by itself whenever the iPhone app does, as long as Automatic Updates is on in the watch's Settings ▸ App Store.
Under these, the watch lists the notes sent lately and how far each has got.

The watch sends everything to Ambitus on your iPhone, which does the work. If the iPhone is out of range, the note or tick waits on the watch and is sent when it is back.
No Wi-Fi or internet is needed. When the iPhone is near, the watch sends by Bluetooth. On a plane, Airplane Mode can switch Bluetooth off. Turn Bluetooth back on in Control Centre, and the watch and iPhone can talk again.
Two complications can be added to a watch face: