OnSong features many ways to share your songs and sets and for years has allowed you to send emails to your team or band. This is done by generating email attachments and then opening the iOS/iPadOS email composition screen with a generated subject and body content. OnSong gives you the ability to attach multiple files for each song, or the ability to compile those attachments into a single attachment or ZIP file.
Starting in iOS/iPadOS 14, users can change their default email app to another app such as Gmail. Per Apple's support documentation, this allows email addresses and links to be opened in the default app. However, the common protocol for opening an email client on computers makes no provision for passing attachments to the e-mail client. It can generate a subject, unformatted body and recipients, but cannot send a formatted body or attachments. Since the design goal of sending an email from the Share Menu in OnSong is to send attachments, OnSong is not able to compose an email with attachments and formatted body content in a third-party email app.
While it could be feasible to integrate various third-party e-mail client SDKs (Software Development Kit which is code and integration points made available by vendors for using their products or services) to discover and open specific e-mail clients on iOS/iPadOS SDK, it appears that none support the ability to create emails with attachments inside of another app without recreating an entire user interface. Additionally, these integrations do not permit sending files to email apps.
One way around these limitations is to use OnSong's Open Screen accessible from the Share Menu. This will allow you to generate various file formats similar to the Email Screen, but presents the build-in iOS/iPadOS activity menu. From here, you can select an app to open such as Gmail to begin composing your email.