[Bug]: mushroom-template-badge not updating picture

[vingerha]

Requirements

• I checked the troubleshooting section in the README to verify that I have the latest Mushroom version.
• I did a search to see if there is a similar issue or if a pull request is open.
• I have read the state of card mod support (in pin issues) and understand card mod support is not provided in this repository.

Current Behavior

Using mushroom-template-badge as header badge, have a reference to a locally stored png that refreshes daily. The badge does not update and remains with the old picture 'forever'.
Only option that I found is a browser cache clean (not: ctrl-F5)
This issue is visible on newest Chrome, Edge, iOS(pad/phone) app

Expected Behavior

No response

Steps To Reproduce

Example badge in header

type: custom:mushroom-template-badge
color: red
picture: /local/pictures/meteo_france_alert_today.png
content: "whatever"
entity: sensor.meteo_france_alerts_06

### Context

YAML state
```yaml

Environment

- Browser: Chrome / Edge 
- HA Version: 2025.5.x
- Mushroom: 4.4.0

Anything else?

No response