Please check the below solution.
I have a list named Clients with a column named "ClientID" which will be used for filtering the Documents in powerapp. This "ClientID" is a lookup column in the DocumentSetLibrary (Library which contains your documents inside document sets for each client).

A PowerApp is created which consists a gallery and an input search text box as shown below. Initially all the documents will be shown in the gallery.

In the input textbox, please remove the value in Default
. You can add it to Hint Text
if you want. Below are screenshots of the formula entered for the gallery Items
.
In my case, the source to the gallery library that contains the document sets (DocumentSetLibrary).
I have filtered the "DocumentSetLibrary" using "IsFolder" because DocumentSet is nothing but a folder so to NOT display document set names in the gallery, the filter is applied as "IsFolder" = false

Run the app and try it.

Note: Please do not forget to replace names of library and fields, with names in your solution.
Please upvote and mark as answer i it helps. Thanks.
To filter only in 1 document set use the below formula on the gallery
If(TextInput1.Text = "", Filter(DocumentSetLibrary, IsFolder = false), Search(Filter(DocumentSetLibrary, IsFolder = false && ClientID.Value = "Client ID which you want to search on"), TextInput1.Text, "{Path}"))