I don't know much about nope.chat, but I do use and self-host my own matrix-whatsapp bridge.
A couple of things to take into account: at the very least, you will be trusting the Matrix server (nope.chat in this case) with all the metadata regarding who are you sending messages to and who's messaging you and when, what rooms/groups are you in, the activity in those rooms, usernames, room names and user pictures. You might algo be sharing other metadata like online or typing status of you and your WhatsApp contacts. Basically the same things you are trusting WhatsApp with.
Also, the bridge has encrypted communication with WhatsApp, but it decrypts everything, so whoever has control of the bridge, could access all the message contents if they wanted to. They also hold your session token, so they could impersonate you. Also. There's the possibility of end-to-bridge encryption so that the Matrix server only sees encrypted blobs for the content to and from the bridge, so that at least the Matrix server won't have access to the content and just metadata. But not all Matrix server providers offer end-to-bridge encryption, so I'd suggest you check that before using any Matrix provider.
TL;DR: whoever controls the bridge, has access to all bridged activity and content. Whoever controls the Matrix server has access to at least the metadata, and if end-to-bridge is not enabled, also the content.