That looks like the classic Irish carpenter’s saw stool and general all purpose form put together with 3“ nails. Due to the periodic shrinking an swelling of seasonal movement around the nails it will work loose. My upgrading of the joinery is as far I can discern from a review of similar Shaker types, unique. As can be seen from the kit below the ends are housed into the top and the side cheeks housed for the ends. This makes for an extremely rack proof construction. Nails and glue were used to fix all parts. The long rebate at the top of the cheeks can be made by running a saw alongside a tacked on lath and chopping to depth. I cleaned up the rebate with a wooden skew rebate plane. This was the standard way prior to power routers and dado heads.
The long rebate in which the top sits brings an added stiffness to the top and I would be quite confident that a 5‘ form would resist flexing even using 1“ nominal deal. The timber I used for this stool was 9x1 treated (tanalised) left over from a shed job. It’s an ugly brown colour so I gave it a rough sanding and a lick of gloss paint (Buckingham). I would have preferred an ivy green but they didn’t have it in small tins. A previous one I made and painted red I bartered for a few bags of hardwood logs. I like barter, it enlivens relationships. Money is a cold transaction. My best barter was two hand-carved spoons for a portabale manual typewriter (Olivetti, Lettera D.L. with accents and umlaut).
Dimensions of Stool: Top: 26x9.75“, Ht. 17.5“, Cheeks: 4.25“