I'm pretty sure 32nd-century salons can figure out the technology to give someone hair extensions.
The question is when and why, though. She's supposed to have been busy all year doing courier work and searching for the cause of the Burn. Where did she find the time and the motivation for something as nonessential as really, really long hair extensions/stimulated growth? Was it something she adopted for some mission, as a disguise or something, and it just stuck?
I have the same issue with Daisy Johnson in Agents of SHIELD season 6. How, in the course of a year of itinerant living aboard Zephyr One searching the backwaters of the galaxy, a journey established in the premiere as arduous, austere, and draining of physical and psychological resources, did Daisy manage to maintain that supermodel-gorgeous blonde-and-purple-dyed coif she sported that season? And more importantly, why? I'm all in favor of women looking great onscreen, but if it's in a context where you'd logically expect a more functional, low-maintenance hairdo, it raises questions that demand answers. (See also the 1977 Logan's Run TV series, where Heather Menzies managed to maintain a perfect Farrah Fawcett hairdo while roaming the post-apocalyptic wilds for months in a small hovercraft.)