I'm just curious, how are standard heats of formation derived? Are they just carefully measured quantities that came from experiments?

Heats of formations are standardized and measured values
They are based on the assumption that for free elements heat of formation is zero under standard conditions
Like
1/2H2(g) + 1/2Cl2(g) ------> HCl (g)
In this case heat of formation is zero on the reactant site and whatever heat is released or consumed , it is assigned to products only.