Ask HN: Adding a side project/startup to LinkedIn when employed full time

I have a side project (startup wannabe) which I've been working on part-time with my co-founder.

I'm currently employed full time for an U.S. based company which expects full dedication (in a remote office).

We're reaching a point where exposure for our startup would be very good, and I have a pretty good LinkedIn network. It would also allow me to highlight all the new technology I've been working on.

On the other side, I'm worried about any legal or personal implications - worst case scenario, the company decides to fire me and not pay me severance (I'm entitled to severance and unemployment in my country except for gross breach of contract, which this might be construed as).

Our project is far from ramen profitability, and I'm the main breadwinner for 2, so I need employment for now :) . We haven't raised any money (we tried getting some seed funding, but we were way too early and had no traction)

My co-founder can add the project to his LinkedIn project without repercussions because he has a part-time employment contract.

Should I try to be a "silent" co-founder? We're thinking of featuring in newspaper articles, should I try not to appear?

Thank you.