Hi @TobiasSQA ,
Based on your description: If anything is in the search field, it should filter the items in the gallery based on that, if not, filter it based on the dropdown.
I have made a test for your reference.
1. Here is my SharePoint List.

2. Select the Gallery Control and try to apply the formula like this:
If(
!IsBlank(TextInput1.Text),
Filter(
datasource,
TextInput1.Text in columnname
),
If(
!IsBlank(Dropdown1.Selected.Value),
Filter(
datasource,
Dropdown1.Selected.Value = choicecoulumnname.Value
),
datasource
)
)
Result Screenshots:


In addition, if you want the search bar and dropdown to work together, maybe you could try the following formula:
Search(
If(
!IsBlank(Dropdown1.Selected.Value),
Filter(
datasource,
Dropdown1.Selected.Value = choicecolumnname.Value
),
datasource
),
TextInput1.Text,
"columnname"
)
Result Screenshot:

Best Regards,
Charlie Choi