The manual for MySQL Proxy 0.8.5 states:
Currently MySQL Proxy is compatible only with MySQL 5.0.1 and later.
It's always risky when documentation says "and later" because that isn't likely to be true for all time. You probably can't use software for Windows 95 just because its documentation says it's compatible with that version of Windows "and later" versions. They simply cannot guarantee compatibility with future software, because they don't know what new features will be added, changed, or removed.
In the case of MySQL Proxy, its last release was in August 2014, over nine years ago as we write this. The GA version of MySQL Server that was current at that time was 5.6.20. That's very old!
I'd guess that your server was updated recently, coinciding with when MySQL Proxy stopped working.
Since that era, MySQL has changed its default authentication protocol. I haven't tested it, but I think it's likely that MySQL Proxy simply cannot connect to newer versions like MySQL 5.7.43.
So your choice now are:
Find an archived version of MySQL 5.6, or whatever version you were using with MySQL Proxy successfully before it was updated.
Try to make the decade-old software work with MySQL 5.7 (which by the way is also out of support as of October 2023). No one will help you with this. It's up to you to get the source code and figure out how to make it work. This might require source level changes.
Switch to a more modern proxy, like ProxySQL or MySQL Router. I have no idea why you are using MySQL Proxy, so I can't advise which one would be suitable for your needs.
Rearchitect your system so you don't need a proxy. Just connect clients directly to the MySQL Server. Again, I don't know why you were using a proxy, so I don't know if this is feasible for you.
The bottom line is that you and probably your predecessors have neglected to maintain current software for years, and now you are stopped in your tracks.
You might want to contact a MySQL consulting provider such as Percona or SeveralNines to analyze your usage and recommend the best solution.