For UCSC specifically, Engineering majors are admitted by major into the Baskin School of Engineering where CS resides.
In general, if the major is in the College of Letters and Sciences, they do not admit by major. If the major is in the College of Engineering, they admit by major. UCB and UCD are the only UC’s which offer a CS major through the College of Letters and Sciences. UCB has a secondary admission process to declare CS. In UCD’s case, CS and CSE are in the Department of Computer science. CSE admits by Academic Department so it appears to be admit by major for CS like the rest of the Engineering majors.
If you check this post, it spells out how each UC campus admits Freshman applicants.