Ok a good question, and I have good and bad news for you. Carbon frames generally are discouraged for use w heavy motors due to the added weight and torque, can be dangerous on a brittle frame unlike metal which can flex. But as more motors get lighter, aka CYC and fazua and paradox, (bafang not yet), its safer on carbon frames. So the best option for you currently is a new motor - CYC photon, weighs about 8lbs total. a battery will weigh 8-9 lbs if you get a mid capacity 15-17ah pack. youd prob want to go with a custom battery that could fit in that triangle space, id do some measurements first. ill give you a tip. the current best battery, using a brand new P42A cell, i have my eye on:

https://bicyclemotorworks.com/product/52v-16-8ah-molicel-p42a-high-current-lithium-ion-e-bike-battery/ its on sale for another week. superior weather and overall performance, more capacity and charge cycles. the one i linked you is the current best bang for buck. 873 watt hours is huge, 30-40 miles range ish. you could go with a 20ah pack for up to 1040 watt hours or maybe 50 ish miles of range.

the bad news is the cost, photon is around $900, but the kit is all inclusive, pick the right chainring for your application. a good battery costs $500-700. but you dont want to cheap out. i wouldnt invest in a bafang when theyre way too heavy and sort of old news. you dont want over 11-14 lb motor on the carbon BB - sure it might handle it for awhile...until CRRAAACK?...also you have to buy the bafang accessories, chainrings are over $100, cranks, sensors, magnets, all the annoying stuff adds up to equal the seemingly more expensive kits. you want as light as possible motor for the bb. theres also one torque sensing throttle motor called hermes its 5.4 lbs for the kit but its $2k itself.

brakes prob need upgrading to some entry level hydraulics at least. overall i get you have an older frame, its fine to use for sure. the industrys on the verge of some new tech in next 1-2 years. personally id rather invest in a new motor, a photon or some breakthrough motor. also, be warned if youre buying a manufactured battery from some chinese sourced company for 300$ if you think youre getting a deal vs $500... youre likely getting cheap stuff, cheap cells, overly heavy, bulky plastic case, shoddy connections, more prone to fail over time. i recommend go custom made on the battery. with proper knowledge on how to charge it right, you can make it last 500-1000 charges, thats an easy 5+ years of riding . heres my 22 alloy stumpy bbshd build, https://www.johnnynerdout.com/forum/general-ebike-forum/victory-part-deux

was a lot of fun and i did a good job with it, but the downside is the kit added 14+8 lbs to a bike that was 38 lbs stock...yikes...it was over 60 lbs and with water, etc. more. The next ideal setup is a 33 lbs or less carbon frame full susp bike, with a 5-6 lb motor kit, just at 40lbs or under, then you tether that p42a battery in a backpack to keep weight off the bike. that gives you a lower dexterity penalty due to the weight being off the frame. but the convenience if that battery fits in the frame is quite nice and keeps the center of gravity low. can always move the better kit to a better bike later too (not easily with bafang sometimes).

anyways some stuff to consider. good luck