Guy is married, but separated - what to do?

My boyfriend is still legally married but he’s been separated from his ex for six months now. She told him she “lost feelings” but then he found out she met someone else. He gave me the name of this new guy, and I stalked, and what he said was true. I saw his ex liking this mans photos and commenting on his posts. She left in October.

Fast forward to March 31st, he met me through a mutual friend. We became close very fast. He stays over a lot. We do everything together. He came clean about everything when we first met and I try not to judge because I have “baggage” too. I’m a single mom. His ex has recently reached out, as in last week (so about a month of me and him talking) and now she wants him back. She said she’s going through all of their furniture and pictures and now she changes her mind and regrets what she has done. He has no interest in reconnecting with her because he said he fought for her for three months and nothing. She broke his heart. He let me read her texts about wanting him back and it was confirmed that she really did leave him for someone else. She called herself a psycho, and said she was an awful person, and said she “didn’t satisfy him sexually”, just a bunch of BS and begging for him back. He ignored these messages and all of a sudden, she’s messaging him saying that he’s awful for moving on quickly, she deserves better, she’s the best thing he’s ever had, etc. He left my name out of it to protect me. He even bought a house a few days AFTER she reached out, here in Indiana. She doesn’t live here in Indiana. She’s military in Germany.

Would you stay or leave?? I’m being overly cautious

Edit: Yes, he filed April 10th, four days after he was allowed to. I’ve seen the paperwork. His court date is this month. I also have seen proof that he bought his new house.