I'm still doing testing and experimentation on the longbow and crossbow, and trying to get some more solid numbers because my original findings were not accurate by a long shot due to how the Test Dummy mod apparently doesn't work all that well with the longbows and crossbows anymore. Not sure why.
In general, you can make Bow Limbs which are used in both bows and crossbows. A Longbow requires two bow limbs, a plate, and a bowstring. A Crossbow requires one bow limb, a plate, a tough tool rod, and a bowstring. As of this post, the bowstring does not affect stats, regardless of what it is made of. This may change in later editions.
To the best of my experimentation, Electrum does the most bonus damage for being relatively rapid fire when used as a bow limb. The exact numbers I am still trying to hack out somewhat more reliably, but for either a longbow or a crossbow, electrum bow limb(s) seems optimal at this time. Steel will do more damage, but has significantly slower draw speed. Feel free to experiment.
The plate is going to affect not a whole lot, so make it out of whatever. Personally, for maximized speed, I go Cobalt. Sure, you can go Paper and put redstone on it if you like, but really, the output is roughly the same (10% reduction in draw speed either way). Alternately, for a more durable bow, use either Wood/Treated Wood for the Ecological trait, or use Obsidian for the Duritae property.
For the crossbow, the tough tool rod, I believe, actually does use the handle multiplier. Here, I'd go ahead and definitely use Cobalt, because of the reduced draw speed on top of a relatively decent handle multiplier. Besides, it's only material cost of 3, so it shouldn't be too expensive.
Crossbows no longer go fully automatic, however they CAN be set up 'bolt action'. Basically, when you fire an already loaded bolt, continue to hold down right-click and it'll reload for you. It's not auto-fire, but it's much more balanced.
As far as arrows go...
I did a post about this earlier, and the basic findings seem to be holding relatively true.
Fletching is going to be a trade off between accuracy and stack size. Feather fletching is most accurate, with no bonus to stack size. Slime fletching of any flavor has bonus to stack size with a cost for accuracy. Leaf has the largest bonus to stack size and largest penalty to accuracy.
As far as the shaft and head, it will depend on if you are making arrows or bolts, because some materials cannot be used in bolt heads due to construction techniques (it has to be able to be molten in a TiCo smeltery to be used as a bolt head).
For arrows, Magma Slime is actually a really good option. It's got a better damage bonus than Steel, and shouldn't be too hard to get your hands on once you get into the nether. Pick up some magma slime dirt and some magma slime saplings, and you can farm it pretty easily. Steel and Prismarine are both tied at third place for raw damage bonus. Prismarine has the jagged property, so as stack size decreases, damage increases. Steel has the bleeding effect which will work on anything that isn't instantly killed. Many is, obviously, the highest damage bonus of any head material. Also one of the hardest to obtain.
For bolts, you can't use Magma Slime or Prismarine, because they won't go in the smeltery and melt down. So basically you have Steel for cheap repairs or Many for maximum damage.
Either way, there's some interesting properties of shafts you need to be aware of:
Wood/Treated Wood. Ecological property WILL work to regenerate your arrows. Handy if you use it intermittently.
Bone has the Splintering property which has a chance(? Maybe? More testing needed) of doubling the arrow. Double damage is double fun.
Endstone basically has a flat trajectory, no more arcing ever. Projectile also effectively 'ender-teleports' to target. We're talking ray-tracing projectile here.
Blaze rod's property is 'floating'. Basically, it has a less-steep arc, but goes slower, giving long-distance targets an opportunity to get out of the way. Use Endstone instead.
So, if you want auto-repairing (albeit slowly), use Treated Wood. If you want maximum potential damage that is at least somewhat RNG dependent, use Bone. If you want ray-tracing projectiles, use Endstone.
Once you build your projectile of choice, you then have three modifiers. However, most of them will be largely irrelevant, so we'll go over what I feel are the two most important.
Nether Quartz, yes, adds Sharpness. How this affects damage is something I am still testing. But really, you may wish to experiment to see if it is even necessary. I'm betting that in most cases, probably not.
Mending Moss. Basically, Mending property, but nerfed. Mends slowly over time as long as it has XP. But hey, do this instead of wood shaft for maximum effect that still repairs itself over time.
Lapis. Yes, it affects drops. Probably not much of an issue, but there ya go.
Reinforced Plate. Yes, it does affect how rapidly your quiver depletes. This might actually be something useful. Unfortunately, without ways to stack it up high enough to get basically infinity arrows, this merely mitigates the repair problem, not negates them. Still... one or two levels of this, plus Mending... might combo well. Still in testing.