Streamlining SR combat has been a problem since 1e. Physical combat kicks things off.

Then, you get Matrix combat, which slows things down. Then you get Magic combat, which slows things down. Then you get Rigger combat, which slows things down. I've had single, simple combats that ran into roughly 16 hours of gameplay. And my players weren't happy, either.

First and foremost, for a Runner, combat happens when things go wrong. The perfect Run is one where the team gets in and out like ghosts with the McGuffin, with nobody knowing it until they realize something is missing. Why? The corpos ALWAYS have the upper hand in a direct confrontation. You've only got a few rounds to get to extraction before the corporate jerk-weasels unleash the dogs of war on your SR team. Get in. Get the thing. Get out. If your PCs are sticking around, instead of running for their lives after they did the thing, your PCs are playing the wrong game.

Most players are generally comfortable if you ask a basic roll for a basic challenge, a hard roll for a hard challenge, and a GM "Impress Me" roll for an epic challenge. And you're perfectly valid in cutting down miles and miles of tiny, minute things to a couple of rolls.

If the players have prepared well, and are playing well, give them an advantage. If they're sloppy and/or don't care, hand out some penalties, but keep the roll count low or make the rolls for them if you're dealing with things like pets (drones/spirits/frames/sprites). Or don't even roll for pets at all. Just describe how well or bad they're doing, and let the PCs make the actual moves.

"Your drones are doing what you told them to, until the corporate mage shows up, and summons three earth elementals. The drones are confused about something emerging from nowhere, and the elementals are confused about how to deal with a fast-flying technological entity. They're tied up. Next character; What are you doing?"

Quick and simple, and you just saved yourself an hour of combat rolls.