Well,

lets say I have that nice design for a ship and would want the Devs to see it and consider it for inclusion in the game. In the past there was a no unsolicited submission rule. I think that is still active. How would one get asked to submit a design, that is not said anywhere I could find.

I don't know if you can submit ship designs without a contest of some sort going on.

Maybe just link some images in the OP and hope the devs see it?

The problem with unsolicited designs and the Internet, is that there's no real 'proof' that the designs you created are 'unique' and is not a copy, or derived from some other work.... This would require extensive 'research' on the part of Cryptic to avoid potential Intellectual Property issues when incorporating into a commercial product such as STO...

You should change the blue lighting to red on your battle cruiser.

He could submit a notarized PDF that the work is his and original. This way if he did lie, they wouldn't be liable.

Doesn't work that way... When people sue, they go after the ones with the deepest pockets...

A notarized seal only notarizes the claim, not the proof of the claim. And a notary service will not, and is not qualified to do, a extensive background check on the material...

I have read somewhere (the EULA or something like that), that they do not want you to send them anything unless there is a competition going on.

I am pretty sure it is to avoid people saying that Cryptic stole their art, and as such do don't want to risk it.

This is likely why there is no address to send it. Could of cause also be just to avoid 100000000 emails with "take my warp 54.9999999 ship with 2000 phazers and 60000000 torpedoes" mails.

if you post your design on the forum, Cryptic may use it in game as by posting it on the cryptic forum you are giving up any rights to it and absolving cryptic of any legal copyright responsibility. However they do not and will not accept unrequested designs from the general public sent to them directly (unless as stated above they have specifically requested submissions, e.g the odyssey competition.)