Thank you for providing a reproduction sample.
On my side I see that a dropdownlist with filter opens and closes as expected. The issue I observe is related to having dropdownlist with filter inside bootstrap vue dialog - on opening the dropdownlist, the filter input is not focused and then clicking somewhere else inside the dialog does not collapse the dropdownlist. Is this the problematic behavior you are describing? If not, please clarify it.
Note that the same scenario is not reproducible when using kendo vue dialog - example - on opening the dropdown the filter input is focused as expected, then clicking outside the dropdown closes it.
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