Copper to PEX connection
Easiest is going to be Push-to-Connect 1/2" Coupling.  You will be able to cut the 1/2" copper and then use the SharkBite Push to Connect Coupling to switch to 1/2" PEX the rest of the way up to your vanity.  Then you will have to figure out how to connect the 1/2" PEX to the sink and include a shut off under the sink.  If you have access to the wall behind the vanity then I like to put 90-Degree Drop-Ear Elbow with a 1/2" Chrome Plated Nipple followed by a 1/2 in. x 3/8 in. Angle Valve.

This Video does a good job of showing it: https://www.youtube.com/watch?v=DL1NL_9Yd1U



https://www.homedepot.com/p/SharkBite-1-2-in-Brass-Push-to-Connect-Coupling-U008LFA/202270492



https://www.homedepot.com/p/SharkBite-1-2-in-Brass-PEX-Barb-x-1-2-in-Female-Pipe-Thread-Adapter-90-Degree-Drop-Ear-Elbow-UC334LFA/202270584



https://www.homedepot.com/p/Everbilt-Lead-Free-Brass-Pipe-Chrome-Plated-Nipple-1-2-in-MIP-x-3-in-802589/207176770



https://www.homedepot.com/p/BrassCraft-1-2-in-FIP-Inlet-x-3-8-in-O-D-Compression-Outlet-1-4-Turn-Angle-Valve-G2R17X-C1/202047053