You absolutely shouldn't feel horrendous and you're a caring parent who stumbled upon something concerning, and now you're trying to help. Reading her diary might not feel great, but she's 12, and your responsibility is her safety and wellbeing, even emotional.
I agree you shouldn’t tell her you read it, especially if it would damage trust. But there are gentle, proactive ways you can support her without making it obvious.
You could subtly shift the household routine. Maybe start making breakfast together before school, frame it as a bonding thing or something you're doing to improve your own habits. Talk openly (but lightly) about strength, energy, and how food fuels our bodies, avoid weight talk altogether.
It could also help to create moments where she feels heard without it being too direct. Ask how she’s feeling in general, if anything's bothering her lately. She might not open up right away, but you’ll be building the space for it.
And yes, shared activities like swimming, dance, or walking are great - not framed as exercise, just as fun things to do together. The goal is to shift her focus without making it about her body.
Also, if she keeps showing signs of low mood or disordered eating, it may be worth gently bringing in a school counsellor or GP without being alarmist.