So with Captain Crimson set’s new level 70 affixes, resource cost reduction translates to better defense and cooldown translates to faster attack speed, IIRC. to more damage (as corrected by JonDubeQC below.
When I socket a topaz into the helm I notice the Defense stat on the character sheet increase. When I socket a diamond into the helm I do not see a Damage stat increase showing on the character sheet. Am I missing something here?
You’re not missing anything.
Multiplicative damage buffs do not display on the character sheet. Think Bane of the Trapped, you do not see that damage buff on the character sheet, right? Captain Crimson is the same way.
As stated, Multiplicative damage buffs (things like BotT, CoE, F&N, EW) are not reflected on the character sheet for damage. This has pretty much always been true.
Damage Reduction on the other hand IS shown and reflected in the toughness stat. The All Damage resist you get from items and bonuses is show as the +green number when you mouse over a resistance. This applies to nearly all damage reduction items (unity is an exception due to its mechanics for example)
Reduce cooldown give more dammage not attack speed.