AutoRestarter handles two everyday situations on its own.
You launched a game on your PC. Steam only lets you be "playing" on one device at a time. The moment you start a game on your own PC, SteamBoost gets kicked off that account. The dashboard marks it as paused and quietly retries every few minutes. When you close your game, the account pops right back to idling - with the same games, persona, and title you had before.
Steam went down. If Steam itself has an outage or restarts for an update, SteamBoost notices, waits for Steam to come back, then reconnects on its own. Same logic, same auto-resume.
Either way, you never have to manually restart anything. It's on by default for every account, on every plan. If you'd rather have accounts go errored instead of auto-resuming, flip it off in your profile settings.