The first aircraft to fly made of composites? The Wright Flyer
Or the Lilienthal Normalsegelapparat. Primary structure made from cellulose fibre reinforced lignin a.k.a. wood.
It is funny to see how the glider industry directly moved from wood to composits applying exactly the same construction principles, while large aircraft industry went via all metal, and forgot about all the basic design methods of (natural) composites, now basically building aircraft from black aluminum, laying up sheet composites, cutting out parts and riveting them together...
Did not realize that so much of the composite work was performed manually.
If you want to use the full potential of the material, this is the way to go. If you just need to compete with conventional metal design, need to keep repairability of the product and labour cost is the driver, then you do a fully automated production of a very simple design.
If you severely damage your fan blade, you anyway replace it. No matter whether metal or composites. So no need to design for easy (riveted...) repair.
Keeping in mind there are composites that shrink when heated, would that conceivably play a part in engine technology?
Only carbon fibre shrinks, and only along its axis. All other fibres and resins do expand. Carbon expands perpendicular to the fibres. You can taylor your thermal deformation according to your need when defining the layup sequence, just like you can taylor strength, stiffness and the mode of deformation. You can make a blade twist when exposed to centrifugal forces, making your fan a constant speed propeller. You can make flaps or control surfaces soft in bending and stiff in twisting, reducing secondary loads and loads on the hinges. This is the major difference to isotropic metal, which has the same stiffnes and thermal expansion in all directions.