I have an old school technique that works just fine, but newer popular techniques often have much lighter pressures, which is why there are so many different suggestions. You are well served to not mix and match, but follow someone who shoots well and master their technique before tweaking and experimenting with changes. Everything is testable to determine what works best for you, but it requires a decent amount of shooting.
With repetition the shoulder pressure will get more consistent over time. Tighter than normal pressure resists movement of the rifle and it will shoot slightly lower on target. Same for less pressure - it allows slightly more vertical movement and groups will hit higher. I get the best groups if the pressure is just firm enough to flatten out any clothing, which also helps keep recoil from slapping the shoulder. It doesn’t requiring straining, but is firm.
Some use light shoulder pressure from the bench or when using a bipod and heavier pressure with other positions or faster shots. I’m a believer in making the shot feel as consistent as possible across all positions so when a high stress situations pops up there’s less chance of an inadvertent mess up. When someone is rushed and literally drops the rifle off the shoulder at the shot, that’s a clue they mixed it up.
The “handshake pressure” on the pistol grip works great for me, but many shooting light recoiling rifles do well with less and I can’t say they are wrong if the target shows good groups. Like shoulder pressure, I’ll always be in favor of consistency and the same handshake pressure.
One step further, I’ve found the best groups and fastest recovery of the sight picture when my off hand is on the forend, beit bench, bipod or shooting off a pack. With heavy recoiling rifles letting the forend go to just flop around at the shot causes many issues, none of which are good.
Anytime your hands are locked onto the stock and the stock is pulled into the shoulder, there’s an art to relaxing the arms enough that subconscious twitches aren’t throwing shots. It can be as bad as a flinch if you’re tensing up as the shot brakes. Smooth follow through is hard to describe, but comes naturally with enough repetition. If someone were to carefully shoot and measure groups off the bench (or bipod) every 1000 rounds, it should show an improvement as muscle memory gets more consistent and the body learns to relax.