That sounds like a bug in how the client handles the store/ad popups. Normally, those windows are just web views pulled from Steam’s servers, but if the request fails or hangs, it can sometimes take down the client’s connection layer along with it. That’s why you suddenly appear offline even though you didn’t switch to Offline Mode yourself.

A few things you can try:
– Clear Steam’s web cache: Steam > Settings > Web Browser > Delete Web Browser Cache/Cookies.
– Opt into (or out of) the Steam Beta Client — many UI bugs like this get fixed in one branch before the other.
– Disable the “Notify me about additions or changes to my games, new releases, and upcoming events” option under Settings > Interface to reduce popups.
– If it still happens, file a report via Help > Steam Support > My Account > Steam Client Issues — Valve won’t know to patch it unless enough reports point to the same bug.

So the ads aren’t crashing your network, it’s just the Steam client choking on its own overlay when fetching the popup. Clearing cache or switching client branches usually helps.