Smooth, flowing surfing is about letting the board dance.
When I used to race enduro/motocross, on fast sections of trail or in the whoops, the fastest way through is to let the bike dance under you. You give inputs and add corrections to get it to do what you want, but if you try to force it, all that happens is you get tired, and/or wad it up. Biggest factor: Stay over the bike.
Power, speed, and flow in surfing is much the same. Since moving to SUP, a major hurdle for me with the bigger board was getting over forcing things. It feels ugly, it's tiring, and you just end up in the water. Once I came around to the fact that it's just not going to work like a shortboard, and dialed it way back, things got much, much better.
Crouching: Two things here. One is lowering the center of mass (balance), the other is storing energy. Stored energy can simply be a part of the flow. Enter "the dance." Board goes up, body (knees, waist, ankles, neck) compresses. Board goes down, everything extends. Or it can be a part of imparting power to the board in a quick release; compress going into the bottom turn, and extend coming out to add energy for moving forward or climbing back up the wave face. Then compress again while going up the wave face. This not only "coils the spring," but it lets the board "float," so it doesn't burn as much energy climbing the wave face. Then coming around the top where the board will try to stall, extend, putting energy (drive) back into keeping the board moving forward. "The dance" is recovering energy where it's given, and giving it back where it's needed, without forcing things. A really hard snap off the top isn't really forced. When done correctly, the board follows the direction of the input, the wave pushes it around, and the body follows. Trick is knowing where the board is going, and keeping the body over it.
How well this is done is simply a matter of time and experience. Some catch on quick, and some will never get it. Beginners can't be expected to "feel" the wave and board, and dance to it. Those with poor knees, etc., can't be expected to put large amounts of stored energy into a turn. The one thing everyone can do to look and feel better is, within reason, to not only keep the center of mass directly over the board, but to keep the mass as close to center as possible. During a hard bottom turn, we might be leaning on the paddle, and the CM might shift off the center of the board a little, but not as much as people might think, and you would never put mass over the high side in order to counter mass put over the low side. "Ugly" surfing that is often seen in beginners is when they try to lower the CG by bending too much at the waist. They counter this by sticking the butt out. CG is lower, and CM may still be centered, but mass is spread latterly. It's more stable than having all the mass directly in the middle, but most consider it ugly. As people get more used to a twitchy board, the more they will tend to move the mass back to the center. Why they don't compress and extend is simply a matter of experience and practice. Feeling the board, and dancing to what it's doing. Give it an input, know what it's going to do, and stay over it.
Bending at the knees. When you bend at the knees, the waist, ankles and neck will also hinge, but you can keep the mass as close to center as possible. IMO this makes for beautiful, good feeling surfing. However, the knees will usually bend forward (towards the front of the board, mostly with the rear knee bent more. Makes sense, as the rear leg is the one that's going to store and release the most energy. The knees also want to come closer together. With a too-wide stance, the rear knee will bend in a different direction, and the knees will spread. Beginner stance often has the front knee going forward, and the rear knee going rearward. Poop stance. Like taking a squat. Feet closer together looks beautiful, but isn't functional in a hard turn. Enter the step-back on the rear foot right before a hard turn. Getting really complex now, which is why it takes many years to get it all put together. Add to that a wide SUP, where you also need to move the feet right and left. A beginner is simply trying not to fall off, and going for stability. Compressing and extending, moving around, etc., comes much later. Got bad knees? Then stand up straight and foot steer. Not a lot of compression and extension, but still beautiful surfing when the feet aren't spread a mile apart, and mass is kept close to the center of the board. Steering a surfboard starts with an input from the feet. You just won't be able to complete some hard turns without imparting energy to the board. So what? Still beautiful and flowing. Leaning should be a reaction to stay over the board. Much like a motorcycle, a turn doesn't start by leaning off of the bike, it starts with an input to the handlebars. The bike starts to lean over, and the body follows to stay above it. When racing, and in a turn, you can then lean your mass well off of the center, the purpose of which is to lower CG, "pulling" mass that wants to stand up, down. We do the same with our paddle on a bottom turn. Properly done, we can put mass lower than could normally be done, making a tighter turn on a larger board possible. Once again, "ugly" surfing involves trying to turn a board with movement of the upper torso; knees locked, feet planted, turning the torso back and forth. Input, board follows, body follows.
Not to be clich?, but if it feels good, it is good. I love seeing the smile on an adult beginner when they get that first wave. It's infectious, and one of the great pleasures of surfing for me; seeing other people really enjoy it. We can all strive to look better at it, up the skill level, etc., but it needs to be for our own satisfaction. Yea, I have an Insta and a Youtube, but only because I'm a team rider with those obligations. If it was all about what others thought, I wouldn't be on a SUP

Speaking of which, another great part of SUP is with the stigma, most have nothing to prove, and it makes for a much friendlier bunch. But I digress.
My biggest hangup is the barrel. It's sooooo much harder than on a shortboard, and I still can't figure out what to do with the accessories

Getting better, but man has it been a challenge. My goal for this year is to finally get the nerve up to take the SUP into some really fat typhoon slabs. I've asked the questions, but answers are wanting... The only help seems to be just bucking up and hucking it. Trial by fire, so to speak.That was a lot to type. I'm not telling anyone how to surf, and many will have other ideas on how it all works. It's an individual thing, and if you're happy, that's really all that matters. I hope it helps someone.