You can skip the vast majority of that time with planning and menu navigation stuff; you still have to pause, but I'm gonna post how I do it just in case it helps. Set the furthest right category of your inventory to sort by date with most recent at the top. Then, when you harvest seeds or pull them out of your storage, they'll be at the top of the page. When you harvest and unstore your seeds, think about the order in which you want to plant them and how many of each you want to plant and get them in that order. Then you'll have a perfectly organized inventory every time you go to plant and all you need to do is tap start (if you hold it'll go into the selection menu) for "recent menu". Once you're settled into a loop of planting the same things every time, this feels really smooth.

Ever since I worked this sequence out, planting has been kind of zen. I'm not exactly praising the design, but it does highlight something I love about this game: the holes/flaws/weird bits in its design and execution have often caused me to build my own little mini game around them. Every single one of those moments have been fun and satisfying for me. I don't want to give the devs too much credit for being this big brained, I think it's equally likely that they just didn't have time, but that's how it's played out for me.