"Chewbacca wasn't given a medal because medals don't really mean much to Wookiees. They don't really put too much credence in them. They have different kinds of ceremonies. The Wookiee Chewbacca was in fact given a great prize and honor during a ceremony with his own people. The whole contingent from the Rebel Alliance went to Chewbacca's people and participated in a very large celebration. It was an honor for the entire Wookiee race."
Anytime a filmmaker says that things happen off screen they making it up.
If they say it was cut and left on the cutting room floor: then it's probably true.
There's a bunch of goofs on IMDB for various Michal Bay films, every goof has a reply along the lines of "there is no reason that [X] couldn't have happened off screen to [resolve gaping plot hole]".
No one claimed the Alliance were free from casual racism. They may be trying, but their personal culture was formed by decades of imperial rule.
Those medals are for "command staff" only. Han is the captain of the MF and Luke is the acting squad leader of Red Squad (you might notice that the veteran, who missed his shot but survived, doesn't get a medal, either.)
I know this is a meme, but I think the simplest answer is filming. Chewy is really tall, if he stands on a lower step, the main cast is all in the same shot.
"There there, Han, me boy. Well done! Look at you! You got a medal and everything, from your little friends! You're such a good little scoundrel, yes you are."
The ceremony takes a few days to put together and due to a mishap the medal for Chewie doesn't arrive. Obviously they can't delay the giant ceremony but Chewie still officially receives a medal.
Being a rebellion and largely on the run Chewie's medal is eventually lost in "the system", sent from rebel base to rebel base. Eventually even Chewie forgets about it and when the New Republic is formed and the filing system updated it truly is lost to "the system".
Eventually when the new rebellion, the Resistance, starts up they fall back to the older rebel filing system. Chewie then finally receives he medal, at the end of Rise of Skywalker.