I can see how you perhaps feel patronised or under suspicion of poor parenting by the teacher suggesting he may not be eating healthily or getting enough sleep. Interesting she preferred to talk rather than explain her concerns in writing by email, which may suggest she knows she’s being a little too interfering.
But it seems to me she’s acting out of concern in making you aware of her observations, which is good practice in terms of child welfare, especially as you hadn’t noticed.
He could well be deficient in iron or some other vitamin or mineral. They need a lot of iron when growing fast and don’t always eat enough iron-rich foods, such as green leafy vegetables, at that age. So, iron tablets can be helpful. I get my kids to take them when run down. Is he vegetarian? This can make it more challenging for teenagers to get enough iron. It could also be dehydration.
Also, are you sure he’s getting to sleep when he goes to bed and not up half the night on his phone?
At 14, he’s a young adult and it’s best to treat him as such. So, I’d tell him the school’s been in touch and ask if he feels tired at school and why he thinks it might be. Could be boredom/concentration.
I’d also suggest he pays a visit to the doctor to get checked out. It may well be that he looks gaunt and tired due to genetics. But it least if he’s had blood tests, you can show the school there’s no apparent problem.