Something similar happened in my relationship recently. My BF kept waking up early in the morning after a 3-4 hour sleep and messed up his sleep hours so he would never have energy to hang out with me in the evening. This happened once a while and never bothered me, but one week it became a regular thing where it'd happen every day. He ended up missing an important commitment both of us had made (hobby related). I questioned him a lot and got "suspicious."
The difference was probably he had lied to me before, so I didn't need much to feel worried since I can kind of "sense" something is off since he's not a great liar. Anyway, long story short, turns out every morning there was a short conversation between him and some other girl from HS, and further search showed that he'd looked up his ex every few months or so. This is an ex from like 5 years ago, too.
In these "conversations" he'd hide my existence from these girls -- would tell her that he's going to work when he's actually going to see me. His "transgressions" are heavier than yours, though I don't think he came close to cheating -- he was simply enjoying attention from a few girls he knew back in HS. Very fishy, but I decided to forgive him and he's regretted it deeply ever since (not that he got "caught", but because he did in the first place). Like you, he also tells me that he doesn't know why he looked his ex up a bunch or why he was overly friendly with the other girl from the same HS.
The hardest part for me to overcome in this was the fact that he seemed to "need" something else in the relationship when we had only been together for about 3 months. I think I'd be OK with him being mildly curious about his past interests (how they're doing rn etc) if it happened like nine or more months into the relationship. Up until that point I thought we had amazing dates and an amazing sex life, so it made little sense that he'd "need" anything else at least after only 2 months or so of us actively having lots of fun.
So the reason why for around 2 weeks I "drilled" him about it (read: had lots of calm conversations) was because I wanted to figure out what exactly he was missing. What did he get out of searching for his ex. What did he get out of those meaningless conversations he had with the other girl, etc. Perhaps your girlfriend feels similar to this -- try to reassure on this front.
PS: If you are adamant about not giving her any reason to feel insecure prior to this incident, she definitely has insecurity issues she carries from previous relationships. It's up to you whether you want to help her deal with it. They need to be resolved though.