Like you I also recently restarted watching SG-1 for the first time since I was a kid. It holds up a lot better than I expected it to. There's the occasional eyerolling cliche (and Carter's dialog about internal vs external gonads is kinda ridiculous) but like you said the cliches are also lampshaded pretty often. I just watched an episode where the Stargate broke and there was an exchange that went something like this—
General Hammond: How long will it take to fix the Stargate?
Technician: It'll be about 24 hours sir
Hammond: You have 12 hours
Technician. Sir, that's not how this works... it'll take about 24 hours
General Hammond: How long will it take to fix the Stargate?
Technician: It'll be about 24 hours sir
Hammond: You have 12 hours
Technician. Sir, that's not how this works... it'll take about 24 hours
Hammond: Oh, okay then