I'm pretty sure you should be using SHA-256. Are you getting that error from the ACME server, or something in your code that's creating the CSR?
This change was announced here; you should subscribe to the API Announcements category if you maintain an ACME client so that you don't get surprised by this sort of thing in the future.
It's still not clear to me exactly what error you're getting where. Is your library returning that it doesn't support that hash method? Or are you actually managing to put an SHA-256 hash in the CSR but getting an error from the ACME server that it doesn't like it?
The text signature algorithm not supported is part of Boulder's error message, so I'm guessing the error is coming from the server.
@grudnitzki1 can you get your software to log the CSR before submission, and share that? CSRs contain public keys, not private keys, so they are safe to share.
Just poking around that documentation site a bit, it looks like what you're looking for might be the CSR's HashAlgorithm method. Though it says that SHA-256 is the default, so I'm sure I don't really know how that library works if you're making SHA-1 hashed CSRs with it if you didn't mean to.
The CSR isn't used directly in the certificate on the web site; the Certificate Authority just uses the public key from it (and a couple other things), and the signature in the CSR (which includes that SHA-256 hash) just validates that the submitter in fact has the corresponding private key. But that signature isn't needed (and wouldn't be useful) in the final certificate. The final certificate has a signature from the CA, and those signatures have been using SHA-256 for a very long time (and you have no control over that part).
Also to make it explicitely clear, although @petercooperjr already explained it as such, any "fancy" detail incorporated into your CSR wouldn't be included into the certificate, unless Let's Encrypt actively does so. E.g., the only "fancy" thing currently added to the certificate if present in the CSR is the "must staple" TLS extension. Anything else is completely ignored.
Well, I have no access to LE's servers (I'm just a random person on the Internet), and while the staff here has been known to dig through logs to solve particularly thorny problems I don't think there's a need for them to do so here. Can't you just point your code at the staging server and see if it still works? You don't need to install the staging certificate on your server, just see if your code can get one.