As far as I can tell, wire is fine regarding privacy. All chat content and metadata is end-to-end encrypted. I am not aware of any additional, unnecessary data collection. You can check their privacy policy at https://start.wire.com/privacy-policy
The main reason for concern comes from the wierd, intransparent move of their holdings company to the US in 2019 (see https://techcrunch.com/2019/11/13/messaging-app-wire-confirms-8-2m-raise-responds-to-privacy-concerns-after-moving-holding-company-to-the-us/ for details)
In 2020 the holdings company moved back to europe and is now located in Germany.
For a comparison with other messengers see https://www.messenger-matrix.de/messenger-matrix-en.html
Full deniability is really difficult. You need to be able to fully trust not only the encryption protocol, but also the company hosting the servers as well as any companies they work with.
The Snowden Leaks as well as the increase in data breaches have shown that that is generally not a good idea.
If you really need deniability I would recommend to look at messengers which do not require any server component and communicate via Tor. One good option might be Briar.