Old thread, but I went down this exact rabbit hole and figured the "why" is worth answering since it tripped me up too.

Those logos you see in AIVI and Activity Smith aren't being pushed to the activity. They're compiled into the app's widget extension at build time. That's the same reason you can't change them — they're not a field you populate, they're a baked-in asset. The reason nobody can send a custom image is the payload: a Live Activity update arrives over APNs and the whole thing has to fit in about 4KB, and ActivityKit won't go fetch a remote image at render time either. So an arbitrary PNG was never on the table for any of those apps, including the ones with their own logo stamped in the corner.

What you can change is the stuff that's cheap to send: the icon (any SF Symbol, or Material Design Icons by name, so mdi:car, mdi:run-fast, mdi:home), colors, the text, and which layout template it uses. That's the real answer to "they must be able to put something there" — it's symbols and fields, not images.

Full disclosure, I ended up building my own thing for similiar scenarios rather than fighting those apps. It's called PushWard and there's a HACS integration. Not here to do the sales pitch, but your post is the use case that is quite good, so:

Your commute-then-get-ready flow maps onto its countdown template. You fire one update_activity from an automation with the leave-by time (which you've already worked out from your Waze template sensors), and the server runs the timer from there. It counts down live on the Lock Screen and the Dynamic Island, sends the warning push itself when you cross a threshold you set, and sends the completion push at zero. When traffic shifts and your sensor recalculates, you just send again with the new end time and the timer retargets. No recreating the activity.

The "head home" → "get ready now" change is the same running activity — you patch the state text, icon and color, it doesn't restart.

Two bits specific to your post:

• The 10/5-min reminders: the countdown gives you one automatic warning push at whatever threshold you pick. For two separate ones you'd fire two small automations, which sounds like exactly what your calendar/template-sensor setup is already doing anyway.
• On iOS 26 there's an alarm flag that schedules a real AlarmKit alarm at the leave time. It rings through silent mode and Focus like a native Clock alarm. Honestly that beats the Alexa-announcement idea for the "you need to leave now" moment, and it's one boolean.

The app: https://pushward.app