The 'could not connect to the Steam network' message at sign-in looks like a Steam outage, and occasionally is, but in most cases the fault sits between the PC and Steam: a router that needs a restart, a VPN or proxy Steam's login rejects, DNS trouble, firewall or antivirus interference, or a corrupted client cache. Check Steam's status first, then work the local list in order.
ipconfig /flushdns in a terminal, and if the router's DNS is suspect, test a public resolver in the network adapter settings.config folder's login data by running Steam with the -login reset is overkill for most; simpler, rename the Steam folder's userdata cache only if support steps fail, or reinstall Steam over itself, keeping the steamapps folder.A sign-in connection error (Steam never reaches the login servers) and a store/community error (signed in, but pages will not load) have different causes. The first is network-path trouble; the second is often Steam's web cache, cleared from Settings, Web Browser, Delete web browser cache, or temporary trouble with Steam's content servers. Naming which one you have halves the work.
Steam is up for everyone else. What is left? Then the fault is in your path: router, ISP, DNS, VPN, or security software, in that rough order of likelihood. Testing from a phone hotspot is the fastest experiment, if Steam connects there, the home network is confirmed as the problem.
Will reinstalling Steam delete my games? Not if the steamapps folder is preserved. Reinstalling over the existing folder, or backing up steamapps first, keeps the library; Steam rediscovers the games when it starts.