Road bike. How far should crank be to the frame?

There is a caveat with symmetry though, as appealing as it might be to the eye, it needs a symmetrical body to be using it to achieve the harmony needed for any serious time on the bike...

The gaps fine, no issue at with that unless you're an absolute animal!
As I mentioned previously, I'd try to get the gap equal on both sides. Physically you won't feel the difference, but psychologically it'll just mess with you're head (if you're anything like me that is).

You could fit a bus through there.

Ah I thought it was second hand.

That looks like 5-7mm or so, that's not ridiculously close. Do you know if the cranks are an aftermarket addition to that bike or the original equiment?

Why would it crash into the frame ? How close is it ? It might bend a bit under power but I doubt you can put it into the frame.

needs pictures from above of both drive side and non drive side when
lined up with the frame .

Is the gap equal on both sides? If no, then it'll need adjusting.

That looks so close, all my bikes I can fit my small finger in between the crank arm and chain stay, take it to your nearest bike shop, don't ride it for now till you get the all clear,

Take a picture not blurred with a measure indicating the gap

Best seen from above as previous reply says..... you & us forum members will get a better view of the query you have to be able an opinion to be given....

I'm worried too, but that's just about your photography. Can't see to offer opinion, too fuzzy I'm afraid. Also will help to take photo directly from above as opposed to at an angle.