As quoted from the Technical Manual: ''Androids display synthesized emotion, superficially register self-awareness and, most importantly of all, have the ability to reason, conceptualize and offer opinion.''
I would also like to list Bishop's banter and knife game with the marines to defend my point of view: https://youtu.be/h-qtqD4PZqY
Those 2 mentions said, in my belief, Synthetics are made to feel (Or pretend they feel) emotions on a superficial level, such levels which would not disrupt the Synthetic in their forays at all but merely make them feel more sociable and ''human'' for easier commingling with people. See Seegson and how they went the other way around on making Synthetics act like soulless machines that had nothing a human like you and me could identify ourselves with, it didn’t end well, can we agree?
To quote the Technical Manual once again and Bishop's video where he can be seen eating: ''Those androids designed for close social interaction with humans are able to eat and drink, though they gain no nutrients from anything they consume. Food and drink is broken down in an artificial stomach cavity, and the resulting liquid is expelled via a retractable catheter.''
Why would a Synthetic feel emotions in a basic level? Why would a Synthetic be able to eat if they gain no benefit from it? Why would a Synthetic have a quirk? And to all these questions I could use the same answer. Just like us humans have different personalities and some ''quirks'' that makes us different from each other and interesting to know, the Synthetics who were built to emulate us so we could feel more comfortable in their presence also have theirs.
Just you imagine if every single Synthetic had the same personality or quirk, much like Seegson did, it would be a bit awkward to work with them.
Anyway, I hope you see where I am coming from.
As for how much they can express these superficial emotions; I say, as long as it doesn’t interfere in their guidelines or duties. Maverick for example, as much as he can appear friendly and welcoming, he holds no real relations or attachments to the soldiers and people that work with him, as in he would not give special treatment or be inherently traumatised if some of them died. He merely shows ''emotion'' because he was made to commingle and work with humans.