I don't think the game natively allows for it without a plugin through something like the Omegga wrapper. This is kinda presumtious of me but it seems like it would an easy plugin to make atleast. After the end of a minigame it just clears the bricks from all the contestants. You'd have to load the map as public to avoid it clearing your bricks when participating yourself. I'm honestly kinda suprised this hasn't made it as some minigame variation, the funcionality is there with bricktionary.
Be aware that in order to use the omegga wrapper to host servers, you'll either need a linux computer you have running seperately from your own that you portforward udp7777 from so people can join, or you use a windows subsystem for linux and keep it there which the README on omegga's github page explains how-to: https://github.com/brickadia-community/omegga
The Omegga README lists alot of methods for you to use. There are commands to get player names with the "getPlayers", then use those names to clear their bricks with "clearBricks", lastly this can be triggered (but I am kinda reaching because I'm not sure how this works myself) "line" Plugin method that will trigger the script once Minigame is ended. Maybe you can even exempt your name from the "clearBricks" thing. I'm probably getting ahead of myself; if you decide to go the omegga route you could join their discord and they'll be alot more help than me.
I get it if this is alot, but I feel like its the closest we're gonna get to what you want to do right now without in-game lua scripting or something similar.
