You can decide on your own in this Case
with the Student residency card you could use Interrail
with your passport you could use Eurail

i would take the Eurailpass as i have with this pass no limit in the Country of Residence.
In your case the UK would be Country of Residence and you would have just one outbound and one inbound journey with Interrail

Since you are resident in the UK, I would suggest the Interrail Pass instead of the Eurail Pass. Residency seems to be the key here rather than national origin

Hi seewulf, in case she takes the Eurrail pass - would it not be checked at the border control for Eurostar that she had a “Eurrail” ticket but a British residency permit?

At Eurostar border control, the police checks your Passport and not the ticket. When you enter Eurostar Gate there are ticket barriers that checks your Reservation. I don’t know if Eurostar Staff will also look on your pass. When I travelled back in 2018 nobody checks my Interrail Pass. 

Thank you, Angelo.