From a company perspective there really is no way to get it right. A restaurant will serve everybody, but you really cannot find one with no alcohol, no pork, no beef, no meat, no seafood, no gluten... you see where it ends, if you cater to every single incompatibility in a big company you will end up in a dark basemeant munching a gray pulp of recycled cardboard as the smallest common denominator. So a restaurant where everybody can order what they like and everybody has to take care of their own problems is the best they can realistically do.
Whether your colleague can or cannot come to this venue is their personal choice. Neither of us can say how comfortable they are with other people around drinking.
However, I'm pretty sure the one thing they don't want is to be in the spotlight about this issue. Neither as the person that didn't come because they were a recovering alcoholic, nor as the person that had to be treated special because they are a recovering alcoholic.
Personally, I don't drink. Not for any specific reason, I just don't like it. It tastes bad, it makes me feel sick, I have to wait for a taxi or shitty public transport home if I don't want to risk my license on a DUI and probably have a hangover the next day. Instead, I prefer to drink something tasty, go home in my own car on time and feel great about it. The average number of times I have to explain that simple truth per evening out is exhausting. People cannot take a "no thank you".
The one thing that makes it easier without spilling any secrets is allies.
Ask whoever prepares that event if the tables are fixed or if you can organize tables with specific wishes. You can have a table that simply has a "no alcohol" rule. That could be all kinds of people. Designated drivers, pregnant women, recovering alcoholics and yes, people like me. Nobody needs to wear a label why they don't want to drink. Nobody needs to explain again and again all evening. No drinks at your table. Period. No questions asked.
If it can be arranged in general, you may want to ask others if they have specific wishes as well. Maybe there will be a vegan table. Or a "no pork" table. Or a "no peanuts" table. People with allergies will have no problem coming forward, because there is no stigma attached to someone allergic to seafood for example. They won't mind being known for that company wide, it's just a fact, like shoe size. Nobody will judge you on it.
So if that is possible, multiple tables with different rules and with no reason needed why you want to be part of that table, that would be great. Just make sure you don't offload the burden of organizing that to the original organizer. If you want it to be a success and want support from the organizer, don't start by telling them they need to work more and harder. That's not going to go over well. Offer your help in doing it.
And obviously don't have the recovering alcoholic lead that effort. Pick someone who is robust enough to say "none of your business" without the fear of any dark secret coming out company wide when anybody asks why they want that.
However, again, whether that specific person is comfortable coming, even with allies, is their choice. They might not be. And that's okay, too.