Permissions issue in Docker SQL Server 2017 while restoring certificate
Is the code shown under "Relevant code:" (in the question) the exact code being executed, as in copied and pasted into here and not re-typed? I ask because the file extension on the sqlserver_backup_cert file is different between the BACKUP and CREATE (i.e. restore) statements. It is backed-up as .cer but then you are looking for .crt in the CREATE.

Also, have you tried skipping files altogether and using hex bytes (i.e. a VARBINARY literal)? You would do the following:

On Prod

SELECT CERTENCODED(CERT_ID(N'sqlserver_backup_cert')) AS [CertificateAndPublicKey],
       CERTPRIVATEKEY(CERT_ID(N'PrivateKeyTest'),
                      'new_password_for_extract(A)',
                      'current_password(B)') AS [PrivateKey];


On Test

CREATE CERTIFICATE [sqlserver_backup_cert]
    FROM BINARY = {output of CERTENCODED}
    WITH PRIVATE KEY (
        BINARY = {output of CERTPRIVATEKEY},
                 DECRYPTION BY PASSWORD = 'new_password_for_extract(A)',
                 ENCRYPTION BY PASSWORD = 'current_password(B)'
                     );


UPDATE

O.P. has confirmed that the issue was indeed the filename extension mismatch.