Open the player's Steam profile and read the rating off the profile page. That is the only reliable answer, because inside CS2 there is no search box for other people's Premier rating. With Pulse installed, a stats panel appears on the profile and shows peak and current Premier rating side by side, each drawn on the background of its own rating tier, so the colour tells you the bracket at a glance. Underneath it lists per-map competitive ranks, and you choose how many of those are shown in the extension's options page.
When it works and when it does not
Two things have to be true. The player must have played rated matches, because an unrated account has no Premier rating to show. And the data has to be public: a private Steam profile, or private match history, shows nothing, in Pulse or in any other tool. Nobody can work around that, and you should be suspicious of anything that claims otherwise. If the panel comes up empty, the usual cause is one of those two, not a bug.
What else the panel shows
Alongside the rating there is a separate in-game section with Private Rank, XP progress and commendations. That part is about the account rather than the skill bracket, and it is useful for the same reason people look up Premier in the first place: judging whether a new teammate is a fresh account or someone who has been playing for years.
Setting it up
Pulse is free, needs no account, no login and no API key, and asks for a single
permission, storage, which it uses to remember your settings. Install it, open any
Steam profile, and the panel is there. Nothing to configure first. What it does with data is
written out in the privacy policy.
Get it for Chrome and Chromium browsers or for Firefox, then check the next profile you were curious about.