I think 2nd tri is ok to do light running since u're alr very active before pregnancy. And on the condition tt ur pregnancy is stable and no complications (best to get ur gynae's advice!) Typically why running not advisable is because there's higher risk of tripping or falling as compared to low impact yoga for example. But I have a friend who still runs 10k in her 7th month as she's a seasoned marathoner. 10k is a much less intense exercise for her tho 😅
There are ppl who exercise all throughout but better you check with your gynae instead of follow other people. Cause every pregnancy and mummy is different