Wood putty won't add any strength. The crack and piece are large enough where seasonal variation would likely cause the putty to separate from the wood anyway.
For sure, clamps are important! There's a gap between the top of the cabinet and the underside of the bench.
I will admit though that's it's sometimes necessary to position the clamp with the bar extending below the surface - in that case not having drawers would be best 👍
I use an inshave (aka scorp), compass plane, curved scrapers, and sandpaper for my seats. It's laborious! Just started on another tonight and of course it has a few stubborn spots.
Good question about the bench. It's a 5" pine top but it dried funny, curving inward at the top. So I inlaid a maple strip to get the front back to square.
We have a Mafter 10" that works great. The handle is kind of primitive feeling but one gets used to it. It totally replaced the 10" stainless All Clad pan which is now lingering in the basement.
I've had my Baratza Virtuoso since 2014-ish and was able to replace the burrs last year. Recommended.