Cross Report drillthrough using a button action

Native cross-report drillthrough only works via right-click. A button's "Drill through" action only lists pages in the same report, which is why the cross-report destination never shows up there - that's expected behaviour, not a setup mistake.

To drive cross-report navigation from a button (and to make it conditional on the selected value), use a Web URL action bound to a measure:

1) Build a measure that returns the destination report URL with URL query-string filters, e.g.:

Target URL = "https://app.powerbi.com/groups/<wsId>/reports/<reportId>/<ReportSection>?filter=Customer/CustomerId eq '" & SELECTEDVALUE(Customer[CustomerId]) & "'"

2) Add a Button, set Action = Web URL, and bind the URL to that measure via the fx (conditional formatting) button. Inside the measure you can branch with SWITCH/IF to send users to different report pages based on the selected fields - that covers your conditional drill-through case.

If you also want to keep the native right-click cross-report drillthrough: both reports must be in the same workspace, the tenant "Cross-report drillthrough" setting must be on, the destination page's drillthrough must have "Cross-report = On", and the drillthrough field must exist with identical table/column names in both models.