People calling the effort you put in to support your partners, friends and family "emotional labor" are either blatantly misinformed or people who want a pass on not giving a shit about their "close ones".

Emotional labor, as a term, was created to explain the difficulties and effort someone has to engage in to regulate their emotions when they're constantly dealing with the suffering of other people during work. It's valid, just as long as you use it in its appropriate context. This dumbass appropriation of the term by a certain branch of liberals is like if someone used the physical concept of entropy to justify why they're never getting out of depression.

If someone only wants emotionless relationships with people they only interact with for their own benefit, and never giving a care in turn, that's legitimate, as long as they don't lie about their intentions. But that might also explain why this Hannah at the OP cannot find a good partner.