Does Elden Ring weapon scaling recalculate if I respec my stats mid-game?

I've been running a Strength build with a heavy weapon, but I want to respec into a Dexterity build using Rennala's rebirth option. My weapon currently shows an S scaling in Strength.

If I reallocate my points into Dexterity, does the weapon's damage automatically recalculate to reflect my new stats, or is the scaling somehow "locked in" from when I first started using it? And do I need to re-apply my Ashes of War / affinity after respeccing, or does that stay intact?