There is a lot of excess lines that fill up the screen and serve no purpose. When it comes to most UIs in all things, regardless of hobby, I tend to like minimalism. It makes the game feel more responsive, optimized, and modern. Destiny has a UI that's much like this and I think nails it.
The quickness/consistency of the UI is important as well. Having a unifying menu system somewhere while in the menu screen that is present at all levels except for the most specific innards of the selection trees is key. This allows for quick navigation to areas of the game. Nobody likes wasting a bunch of time slogging through deep menu trees to do an action, then navigating all the way back out to a main menu, then back in to whatever activity you'd like to do next.
*Have the Play, Customize, Shop menu bar in the top be available at all times. The tree level it should disappear at is the socket portion of the Armor Hall/Weapons Bench/Vehicle Bay. For the Body AI menu, it should disappear when you click on an option within (eg. Prostheses, AI Model, Etc.)
This saves the player from hitting multiple back buttons when going between menus and holding up that illusion of ease of access rather than deep menu diving every time you want to customize your spartan.
The Season Progress button in the bottom left of the main menu is pointless and adds more clutter to the screen.
*Combine the Battle Pass banner in the top right with the functionality of the Season Progress button. One dedicated way to view all season related items/progress/battle pass.
*Swap the Player information tab in the bottom right (Emblem, Player Card, Friends/Party) and swap it with the Battle pass banner. Then have that player information tab look and function exactly like the fireteam banned within the multiplayer tab. Having your name and customized identifiers atop/next to your customized spartan makes sense and would flow better visually.
*Add the options button as a main menu tab. (Apart of the Play, Customize, Shop) The insides of the Options Menu performs exactly like the menus inside each of the Play, Customize, and Shop tabs, good consistency there, so it should be a primary main menu tab.
*The entire bottom darkened banner space should be a dedicated space to showing matchmaking/countdown/level loading/progress bars. That being said when none of those things are going on that bar should completely disappear. Less is more. I feel removing this bottom bar would actually clean up the main menu and make it feel way less cluttered.
*The fine lines language you're using with the UI design is almost there. I would say take out the "breaks/shade changes" of the lining you've used and make them full. An example of what I mean to better explain this is on the Plus button to add more fireteam members within the multiplayer menu page. Just make it one solid white line going around the button without any breaks. These lines are already small enough that adding excess design of similar scale appears messy. Same with the line above the Player banner/below Fireteam #/28. I probably could've explained this one better so I apologize in advanced.
Really not a fan of it not showing your teammates/what their spartan looks like in the lobby before loading into the match. That feature should definitely be brought back.
Empty space is Ok! It's not a bad thing! Minimalism is in! I like what I'm seeing so far so keep up the hard work! <3