Two separate problems are mixed together here, and only one of them actually needs PSBC.
Media and hotfixes don't. The cumulative update download is the install media — extract a CU package and it contains a DVD folder with the complete product: setup.exe, the platform upgrade tools, the Microsoft extensions under Applications, and Base Application.Source.zip. There's no separate media download to chase. Open the Released Updates page for the version you want, follow the KB to its Download Center entry, take your country package, and run setup.exe out of the DVD folder. None of that sits behind a partner login, which is why the earlier answer pointing you at the update pages is the right one for this half.
If you need a specific build rather than the latest CU for a version, BcContainerHelper will give you the exact artifacts — Get-BCArtifactUrl -type OnPrem -version 20.15 -country de. Handy when you're pinning a build for an upgrade hop.
The licence file is the part that genuinely needs PSBC, and it's worth separating out in whatever conversation you're having with Microsoft. Asking for "PSBC access" will get you bounced between teams; asking for the .bclicense for your on-premises purchase gets you routed.
On the two numbers: they're CustomerSource/PartnerSource identifiers from the pre-tenant licensing system, which is exactly why they aren't in the Microsoft 365 admin center. That's not a missing page, it's a different system, and the numbers aren't something you can derive. Whoever sold you the on-premises licence holds them, and can usually either look them up or generate the licence file for you directly. If there's no reselling partner in the picture, it's a licensing support ticket against your agreement rather than a self-service registration.
One thing worth checking before you spend more time on this: v19 through v22 are all past their final cumulative update.
