New Healing Spells (Works on anything?)

The new Cure Wounds and Healing Word does not say that is excludes Undead and Constructs now, so does that mean I can Cure Wounds my Fractal Mascot or an Animated Sword RAW?

Yes.

It's also consistent with the change mentioned in 2024 Paladin vs. 2014 Paladin: What’s New | Dungeons & Dragons about Lay on Hands:

Additionally, Lay on Hands can remove the Poisoned condition and can now be used on Constructs and Undead.

Also, a related thread about the topic:

• Does healing magic/potions harm undead creatures? - Rules & Game Mechanics 

EDIT: for clarity.

They're making Warforged Constructs in the new Eberron book iirc, and looking at the trend in general they seem to be looking to use more creature types for PC races, so it seems likely they dialed back the restrictions on CW and such in anticipation of that move.