Barbara is a better hydro healer than kokomi. Her E healing has longer duration at 15s. With her passive this can increase to 20s (if the party obtains energy particles). With her C2 her cd is reduced by 15% from 32s to 27.2s, giving her a 7.2s downtime (compared to kokomi's 8s downtime).
Her Q heals the whole party, without having to stay on-field and NA as with kokomi. And her C6 can revive fallen party members, something kokomi can never do. To give an idea on how much her Q can heal, at lv13 it regenerates 37.4% HP + 4659.69. If Barbara has 30k hp (easy to achieve as she ascends with hp too), then this is a 15879.69 hp party-wide heal. Most characters at lv90 will have around 15k-20k hp if they are not hp-scaling, so Barbara's burst basically heals all their hp. For comparison this is nearly twice as much as baizhu's E (the party-wide heal).
With C1 she regenerates 1 energy every 10s. So by doing nothing, it would take 800s (~13 minutes) to get her burst up from 0. Another passive reduces stamina consumption by 12% with her E (perhaps this matters for hu tao, since most other dps that are actually meta like Itto, Scaramouche do not need stamina for CA).
Weapons that can be used are the TTDS, prototype amber, ER catalysts, hp catalysts. Apparently dps Barbara is a thing (her CA has 300% scaling at lv10), so perhaps dps catalysts like widsith, kagura can work.
Artifacts include the 4p ocean clam set or 4p maiden's. 2p tenacity, 2p dehya set can also work.
Her C2 also gives 15% hydro dmg bonus so she can be paired with hydro dps like Childe, Yelan, etc. With TTDS she can support many on-field hypercarries such as Xiao, Itto, Cyno, Scaramouche, etc. that have longer dps windows. Her other main use is in hyperbloom teams (and Nilou bloom teams).
Barbara's older sister is Jean. Barbara is also a singer with a fan club, and Albert idolizes her.