Only issue leaving machine like Silvia (that doesn't have auto-fill) on long periods is potentially frying the heating element if boiler water level goes too low. Even that shouldn't happen if over temp trips as it's supposed to. Didn't mention cold shot so that likely didn't happen. How's the shot temps? Don't still own a Silvia but did ~4 years before upgrading. Left her on overnight a number of times without an issue. I routinely would leave her on all day on the weekends. Really don't think your fast shot time problem is related. You've tightened the grind? What's your temp surf routine? Has it needed to be changed? Do you have a PF gauge to check pressure and adjust OPV if necessary? Newer Silvia's have adjustable OPV while the older models (like mine was) required using washer spacers to lower from usually way over 9bar factory stock setting. Mine was around 14bar no flow, made her much more challenging before adjusting! And shots much edgier too...

I leave my Silvia on days at a time. I do keep the water level high and have a PID kit installed. I also always leave the portafilter locked in so as to not dry out the gaskets. I think as of right now, I haven't shutoff the Silvia for a full 7 days.

You've been lucky. If just once steam wand not cranked down tight enough resulting in slow drip over night boiler will go dry. Silvia does not have auto-fill, as in the boiler only fills when pump manually activated for a shot. Having plenty of water in the tank means squat. Even doing a whole bunch of streaming without running the pump periodically can run the boiler dry.

Leaving PF in group won't keep group gasket from drying out. In fact leaving machine on 24/7 will greatly reduce group gasket life, it's the heat that hardens the gasket.