Check if your Garry's Mod server is online
Garry's Mod replies over the standard Source query protocol, so when the check fails it is nearly always a firewall and very rarely the game.
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The ports Garry's Mod uses
Queries use UDP on the very port players join on, which makes this simpler than most games on the list: one port, one protocol. A TCP-only rule can look fine in a quick test and still fail every query.
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Still offline? Try this
Open port, failed query: the addon collection is the next suspect. Until a big collection has finished mounting at boot, nothing replies — and a startup Lua error can leave the process alive but permanently unqueryable.