Do you allow her to take devices into her bedroom in the evening?
Using tech at night unsupervised time wise, would likely be causing more tiredness than a long week of travel etc?
We have a policy of no devices in the bedroom at all, and strictly controlled time on the weekend.Extra time must be earned through jobs, completing school work etc. Self-esteem problems are far more likely in teenage girls from internet usage ( Instagram, Snapchat , Discord etc) than from simply going to PE.
I don't think you are being too harsh at all removing her devices and I would continue to do so. Continue either inpluging and removing your router/ or switch passwords so she cannot sneak down to use the main computer. Limit time, no devices in bedroom and at least an hour clear of all tech usage before bed.
The threat change schools is a bad one and may well not be necessary if you address her problems with Discord etc,Disrupting a child during their high school years is an awful thing to do ( speaking from personal experience) whether it be a shift to a state school or a private school.
If she tries claiming illness again, don't excuse her for that reason with the school. Tell them she refuses to go.
Send her to a counsellor by all means if she is requesting one, but tie her internet usage into going to school on Fridays.
I work in social media education, and there are some very negative studies coming out about self-esteem, and mental health world wide for children, all these studies reflect the length of time spent using these applications being the issue. People forget that social media has only really been around for 7-10 years . It's a social experiment with no parameters and no real long term studies. What studies there are have some serious implications especially for teens.
Dm me if you would like some links to relevant studies.