Prior to Yamato leaving there were different uniforms for different services, and they seemed to have a dress uniform of sorts. But I think the only person we see wearing one is Niimi in the scene where Okita is addressing the crew before they board Yamato. Most of the rest have jumpsuits and scarves. They only reason I that might be a dress uniform is that she is wearing a tie. Post-Yamato? They seem to still have those uniforms in early 2202, with a few color changes (the red uniforms from 2199 are now grey/white) and the coats seem to remain for some officers. These uniforms seem to have remained consistent for non-Yamato, non-Task Force 65, and non-Ginga personnel. Ginga has its own inversed uniform, while members on Hyuga, Asuka, and Yamato have the Yamato uniforms. In 2202 there appears to be a jumpsuit uniform you see Sanada and others wearing early on. But at the memorial at the end of the series, they are all in more formal looking uniforms that are not Yamato crew uniforms.
As of 2205, the Task Force 65 crew members at the ceremony are all in Yamato regular uniforms, with the captains in coats. Even the captains of other ships that are not going on the mission are in coats. The basic problem with an assessment on dress uniforms is that we hardly see the regular Navy uniforms up close in these situations to tell if there is a difference, since the focus is Yamato's crew. The Yamato crew uniforms are not dress but they are special assignment uniforms. The last time we get a good look at regular Navy uniforms is in 2202, with some in 3199 at headquarters during the invasion. Shima's group were in Earth Federation Air Force uniforms while working with the Automated Fleet. Yuki was in her grey/white uniform while at headquarters. But pretty much all the other regulars in uniform were in Task Force 65 uniforms or were on Ginga.