In the first full series trailer that dropped after the character spotlight shorts at the beginning of April there’s a quick shot of Pike in bed with a woman with hair that’s much longer and curlier than Melanie Scrofano’s as Captain Batel.
It could be her just with longer hair, but something about the body language of the woman in the blink-and-you’d-miss-it scene with Pike in bed from the trailer, when she playfully pats/slaps Pike makes me think it’s a different actor playing a different character.
Between that glimpse that seems to show Pike with someone else, and the exchange between Batel and Pike over breakfast, with Pike saying “So give me a call, we'll get together,” makes me think Pike and Batel are a fairly casual relationship, and not necessarily too serious, or exclusive/monogamous.