How can I recover data from my HP Stream 14-cb172wm

Your best bet will be to open the machine and disconnect the internal panel from the motherboard, and hook the machine up to a TV or external monitor. When you remove the internal display from an HP, then it will kick back to an external display by default. As far as the adaper, any slim barrel HP adapter like the 65W used by the older Pavilions will work - just needs the 4.5mm tip.

Yours is straightforward to open - remove the screws from the bottom, pry the bottom cover off and find the big metal connector near the front of the laptop as you have it opened. You will need to disconnect the battery first otherwise you could blow the display backlight fuse. Use this guide to get the bottom cover off: HP Stream 14-CB174WM Lower Case Replacement

This laptop is effectively manufactured e-waste, considering the parts cost compared to the new device cost, so I wouldn’t worry if you break a clip or two, unless you really want to preserve it for repair. The other issue is if you do not repair it there is not a good way to wipe eMMC (the 64GB ones are like SD cards, but managed so you can't wipe them with an SD card format tool, 128GB UFS ones MIGHT have some secure erase options) on these as they do not have proper secure erase support through AHCI or JEDEC standard commands for eMMC :-(. The only way I know to do it is by knowing how to run the dd or shred Linux commands, or by using a tool that automates it, like Parted Magic, or pray some option exists that works and isn't priced sky high like Blancco - even I don't maintain a Blancco license! I would rather dd these things given the cost of a license vs a one off freak someone wants erased!