I mean maybe I'm just wired differently but this looks pretty fine for any bike? Water seems to be only about 20cm deep and the ground below is relatively even stones. And on the other side, the path goes up fine.
Looks to be shallow enough to (at least mostly) avoid getting wet feet and the bottom looks firm, I'd give it a go without worrying too much. Could be awkward with the skinny tyres of a road bike but I'm assuming from the lead in and out being dirt that this is a track where one has at least brought a gravel bike.
I had to. It is few weeks old foto - behind me is steep gravel downhill and you see this streem in the last moment so I had to slam my brakes. One side had pretty big stones so if I didn't check it I would end up in it.
If it's just a one time road block and you don't want to drive through the water, you could have still get out of your shoes and carry the bike over there. On the left side you could probably even hop from trunk to trunk.
The path looks nice and thanks to the little creek, it's probably less crowded. ;)
I wonder how it looked like when it was actually marked as a bikeable trail. I can imagine the amount of water changes throughout the seasons. Or years. Or aeons.