I am seeing what I believe is the same issue on Pop 24.04. Download progress shows as ~1-3% in spite of 30 minutes of downloading at pretty solid disk (up to 1.2 gbps), and download (up to 697 mbps) speeds.
Also using Linux Mint (22.1 Cinnamon) -- the progress bar (both at the bottom of the client and on the downloads screen) is always 0%, no matter if it's downloading or installing. Pausing the process shows the percentage, resuming makes it display 0% again. No network activity is displayed on the downloads screen either, despite it clearly downloading content in the background.
Nothing extracted yet.
Using both the stable and beta versions of steam when downloading an update, game, workshop item, or anything in-general the progress bar won't update on what percentage of the download is at and to see it I have to pause the download see the current percentage then resume then it'll be stuck again until it's finished or I pause again.
Using Linux mint 22.2 Cinnamon.