I understand it to mean both of those things. Shakespeare managed to pack a lot of meaning into his words. He would have been aware of all the possible senses.
If you wish to answer the question for yourself, think about what the nature of heart is in metaphor.
If we set aside science and medicine, the word 'heart' is most often used in relation to love and to courage.
The following website archives many sayings about the heart.
Heart Quotes and Proverbs
The word 'courage' derives ultimately from the Latin 'cor' meaning 'heart'.
courage (n.) Look up courage at Dictionary.comc. 1300, from Old French
corage (12c., Modern French courage) "heart, innermost feelings;
temper," from Vulgar Latin *coraticum (source of Italian coraggio,
Spanish coraje), from Latin cor "heart," from PIE root *kerd- (1)
"heart" (see heart (n.)) which remains a common metaphor for inner
strength. In Middle English, used broadly for "what is in one's mind
or thoughts," hence "bravery," but also "wrath, pride, confidence,
lustiness," or any sort of inclination. Replaced Old English ellen,
which also meant "zeal, strength."