Log4shell exploit

Is Vaultwarden effected by the log4shell exploit?

Vaultwarden is written in Rust.
The exploit you are referring too is for the Java language.

And the bundled web vault is mainly written in TypeScript which is also not affected by this vulnerability.

Log4shell will probably affect Apache if used for the reverse proxy.

It does not affect Apache httpd, which is what the web server/reverse proxy software is called. It’s not written in Java, ergo, not affected.