This is extremely irresponsible advice for anyone who isn't already skilled in securing their systems and keeping their software up to date. Skimming through that video, there's no thought given to securing the OS, "pi" account is effectively given root access (through "docker" group) with a default password of "raspberry", network access is unrestricted, there's no thought given to secure remote access (e.g. a VPN), there are no auto-updates for either the OS or vaultwarden, leaving you exposed in case of future vulnerabilities.
I've given up trying to self host stuff like that, it's always a nightmare compared to paying for the service. Plausible Analytics being a prime example.
I would say that in the case of analytics, there are more things to consider than price and ease of installation when considering self-hosting. By not self-hosting you are sending your users data to a 3rd party, which might have impact on their privacy or on the law compliance.
What you are referring to is essentially a compatible server implementation called "Vaultwarden" (formerly Bitwarden_rs), where the original company will see no money whatsoever.
This is an excellent step by step tutorial that tells you how to self host it: https://www.youtube.com/watch?v=eCJA1F72izc