I've only tested this on a Google Pixel device, but it works reliably enough for me to want to share.

1. Tap the unresponsible bottom left picture icon in the app.
   
2. Immediately after doing that, switch apps or go to the home screen.
   
3. Switch back again to the chat app without tapping anything and it should open the menu to allow uploading images again.

You'll have to do this every time you want to send an image. If this solution still doesn't work for you, then you should check your app permissions and make sure steam has full access to your media files.