Is my boyfriend cheating on me? And what should I do?

So my boyfriend (40m) that l’ve (38f) know for a few years told me the yesterday about this girl (30f) who’s in the gym with him and who apparently over a year ago she was checking him out when they were together in the gym. then they were introduced to each other by someone they both knew and this girl asks my boyfriend for his number because she wanted to be his gym buddy! they do exchange numbers so she could call him when she’s there so they could workout together he tells me. Anyway they got talking and working out a couple of times together and he learned some stuff about her like her age and what she do for a living and this kind of stuff. later on he says the girl suddenly stopped taking to him he doesn’t know why and he doesn’t ask her for explanation because he doesn’t care and he learns she got engaged, and he checks her profile photo and see that she did really get engaged. he’s telling me that she’s at this point still checking him out in the gym but not talking to him and that she was following every states he uploaded and yesterday (literally the day he tells me all of this) he apparently posted some song on his states and the girl saw it and when she saw him at the gym yesterday she walked by him checking him out like she wanted him to talk to her but didn’t say a word to him. so he was puzzled by her actions and why is she checking him out if she’s engaged and if she stopped talking to him after they hanged out a “couple of times” ! and why was she seeing and checking all his states . He just wanted to know what does she want from him . Now he’s telling me all of this so I could figure it out for him which makes me do angry mind you I can’t see these states he’s posting and I didn’t even know about them !! and where he posted them !! my guess is on WhatsApp since she has his phone number. Anyway today he tells me that he purposely posted some states to get her to block him and end this whole situation with her! Like what situation is this!!!
and she did immediately block him and he was laughing and saying (I wanted her to block me ) so I asked him what did he post and after I asked over and over he said a picture of us . He never ever in all the time I’ve known him posted a pic of me not to his socials not to anything which is a red flag in itself I know but I always thought that it was due to me being private and shy. but when I asked him why he posted us he said I wanted her to know I was taken !!! Like now you wanted her to know you were taken !!! Wtf am I supposed to think about all of this ? he cheated on me with this girl right !!! ?? But why tell me about this whole thing though if he did ?

TL;DR: boyfriend meets a gym buddy and tells me about her now . Was he cheating?