I'm not an app developer, so I don't 100% know the full story here, but you'll have to sign your app package with your own signing certificate, trust the cert or [preferably] the cert issuer/chain (this is automatic if using a cert issued by a third party public CA), and then enable side loading on these devices.
To sign your packages, you can use Azure Key Vault: Sign packages with Azure Key Vault - MSIX | Microsoft Learn
You can use the Trusted Signing service (Trusted Signing is in Public Preview - Microsoft Community Hub) to get a signing certificate or you can get one from a trusted public CA. I don't recommend using a self-signed cert. You could also use an internal PKI if you have one.
See Sideload line of business apps | Microsoft Learn for more info on side-loading apps which can be done with Intune.
I fully acknowledge that this is probably more complex conceptually, but it does skip uploading it anywhere and then downloading it again just to sign it giving you control of the entire process. This was one of the minor use cases that the Microsoft Store for Business enabled that was not replaced by anything else directly to my knowledge ("minor" here in terms of overall customer usage and not importance).