I remember reading your posts during the incident, you mentioned you are quite familiar with the sort of server architecture steam is using.
I take it you believe it's safe to log in and change our account info. Would you recommend logging out afterwards?
I am not familiar with the specific server architecture, I just happen to work in web development (but definitely not as a sysadmin!). I probably know just enough to be dangerous in most cases.
I actually couldn't tell you if it's safe to log in and change your account info, only that the single statement Valve has released about the incident suggests the problem has been fixed. This is corroborated by the lack of any new reports of the problem. Going to your account page is still a risk, given how the leak occurred last time (basically, you visiting the page could mean that a cache is storing that response, which could then be served to others later). However, if we take Valve at their word and the caching configuration error is gone, then either your pages aren't in cache at all or they're in a per-user cache that shouldn't be displayed to other users or guests.
Moreover, at this point, the sooner you access those pages, the sooner they'll leave any caching system if indeed those pages are still cached. I suspect they aren't, because there's no reason to ever cache those pages in such a way that leaves identifying information intact, but since Valve hasn't told us anything about the nature of the problem or the solution we can only assume the worst and hope for the best.
Early reports suggested the best thing you could do was log out of Steam and not view any store pages. I think that advice was given by SteamDB (note: NOT affiliated with Steam, they are a third-party site) because of the aforementioned cache, where visiting your own account pages legitimately could get your pages into the publicly accessible cache. There's no evidence that being logged in or out is a vulnerability in itself, so I don't think you need to worry about your login status for now.
tl;dr: I think it's about as safe as it's going to be to log in and change your account, short of another official statement from Valve. You probably don't need to worry about logging out, either. However, I wouldn't blame you if you chose to exercise extreme caution and just stay out of Steam for a while longer; evidence suggests your information is still there even if you remove your payment info.
