Not Jessica but I’ve given copies of my passport before. It’s just to verify your identity. If it is a reputable agency I wouldn’t be too concerned.
Perfectly normal they need to see that you have the right to work here and also general information to be checked.
Very common - in fact, they normally need to see the real thing and then take a photocopy of it, although Covid has lightened the regulations around this.
If they don't check your right to work in the UK with a photo (which can only really be done by a passport) they could be fined £10k even if you actually have the right to work in the UK.
Thank you all for the responses! Definitely made me feel better to move forward with this.