There is currently no way in Battlefield 2042 to see how well you're doing against the rest of the server, but there could be.
DICE elected not to bring back a number of classic features when developing Battlefield 2042. One of those is the standard scoreboard, which typically shows your place amongst your team, as well as enemy players.
Battlefield 2042's version of that only really tracks your own performance, and offers general guidance on how the rest of the squads on your team are doing. There's no way to benchmark your own performance against everyone else's. Though the game does have more pressing issues that need to be dealt with, players have been lamenting the death of the scoreboard since before Battlefield 2042 even launched.
DICE eventually sort-of acknowledged the community's desire for a traditional scoreboard, but the version we might get down the line will likely only show up at the end of the round. As the Battlefield community is known to do, some of the more industrial members have been coming up with their own solutions.
We just recently saw an impressive redesign of the deploy screen, and now it’s the scoreboard's turn. Reddit user PowaPop came up with a fairly basic design of what the scoreboard could look, using much of the same design language utilised by the rest of the game's UI.
This version is designed to be shown at the end of the match, as a separate page before the ribbon round-up. The layout has enough room for kills, assists, revives and an overall score for each player.
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Previous iterations of the Battlefield scoreboard included more details, but they seem to get slimmer with every new game. Nevertheless, this design could be a decent compromise, and doesn't even extensively change the look, as we've seen with other community-made projects.
DICE recently rolled out Battlefield 2042's last patch this year, as the studio prepares for the holiday break. The update, while smaller than its predecessor, did bring a number of welcome balance tweaks and major changes to Breakthrough on certain maps.