Is my headtube unusually long?
Based on the image, I will assume this is some kind of 61-63CM or XL to XXL trekking/hybrid bike. If true, no, your head tube is not unusually long for the size and type of bike you have.
You also say you want ligher. Replacing what you have with any suspension fork, but especially with a basic one, won't do that.
If you really want to go with a cheap suspension fork, the main way to handle this situation I know of would be one of the RST 300mm steerers, which to my awareness can be transplanted into most or all of their straight 1-1/8&quot; 700 hybrid/trekking/urban type forks. (It's been a while since I've had to mess with this so I don't know the current compatibility rules in their lineup for what can and can't take the 300mm aftermarket steerers they sell; you would need to do that research to be safe.)
Otherwise your off the shelf options would be various rigid forks, which are easy to find in 300mm.