yep. the security is in the hands of the client.
apple in general is extremely good with handling this, actually mobile in general.
however, if a web client is poorly coded, you can trick the website into loading a script. if you can run a script on the browser, you'll be able to steal cookies / private keys etc
however, if you're using mobile, then the security risk of nostr is the same as any other social media that allows exchange of free form text