Steam's been giving me a lot of errors over the past few days, primarily relating to staying signed into friends and also giving me error messages when trying to trade with others (I don't have any trade bans in place that I am aware of.) I read that this can be related to cookies in the browser and/or client so I reinstalled steam and cleared my settings for my web browser. Steam, as it always has, believes my current machine to now be a "new device" (it's not, it's the same one I've always used) and has decided to completely prevent me from trading items for the next 7 days. I understand Steam has been self-destructing on a semi-regular basis recently, so that's probably the root cause of my original issue, but my question is, I also have 2 other devices that are authorised for Steam (prior to this incident), will those devices be allow to perform trading or is the 7 day trading restriction applied to the entire account?
The trading restriction is account-based. Signing in on a new device shouldn't impose a trading restriction if you've had Steam Guard enabled for more than two weeks, so submit a ticket and be sure to explain your situation thoroughly (though regardless of the where the fault lies you may be asked to just ride it out).
Edit: To be clear, Valve says that the "cooldown" shouldn't affect devices within the same "household" (i.e. those that share the same IP address), but I've since signed in from quite a few new devices at mates' places and haven't had an issue.