When shifting both left and right shifters, what's the preferred sequence? My technique has always been "easier, then harder".  When switching to the big chain ring, I first downshift at least twice on the right (easier) and then upshift on the left (harder).  When switching to the small chain ring, I first downshift on the left (easier) and then upshift at least twice on the right (harder).  I find this technique effective because it maintains my cadence and prevents loss of momentum in my legs, especially important when switching to the big chain ring.

Does my technique hold water?
It doesn't really work to ask or answer this question independent of rear cluster gear count, range, and chainring tooth difference. In particular, road compact vs standard front gap leads to totally different strategies with shifting.

The more gears in back for a given cluster range, the less downside there is to just staying in the same chainring chosen based on the terrain you're in. The technically most optimal gear may still be on another ring, but there are efficiency and enjoyment downsides to doing all that back and forth shifting to stay on top of it. This effect has increased marginally with each speed generation.

The greater the chainring gap, the more rear shifting you need to do if you insist on sequencing your gearing exactly. That's a big reason why compact really took off in the days of 10 speed and not 5 speed - with 5 speed rear ends you're priced in to doing that sequencing, but with 10 it matters a lot less.

Also the greater the ring gap, the more gear values you're going to have back to back on the same ring at the extremes of the bike's gear range. For example, on 11-speed 34-50 11-25, the top 6 or so gears are all on the large ring and the bottom 4 or so are all on the small, so there's going to be a lot of the time where the most optimal sequencing involves no front shifting at all. Compare that to five-speed 42-52 13-25, where the only the top 1 or 2 and bottom 1 or 2 gears are on their respective chainrings. Again, you're then priced in to hunting around.

If you want to master this topic, studying different setups in a gearing calculator like https://www.sheldonbrown.com/gear-calc.html is a good idea.