@Desbrina
You can try to modify your formula to use the Search function instead of using the in operator, since the Search function allows partial text matching. Here is an updated version of your formula:
SortByColumns(
Filter(
_ClubInfo,
IsBlank(SearchBox.Text) || Search(SearchBox.Text, Name) || Search(SearchBox.Text, Prefix) || Search(SearchBox.Text, Site)
),
"Name",
SortOrder.Ascending
)
The Search function should return all the items where SearchBox.Text is a substring of Name, Prefix, or Site which should give you results when you type in a partial name.
If you prefer to see what something starts with, use StartsWith function to check if the Name or Prefix or Site starts with the string entered in the SearchBox.Text. Here's an example of how you can implement this:
SortByColumns(
Filter(
_ClubInfo,
IsBlank(SearchBox.Text) || StartsWith(Name, SearchBox.Text) || StartsWith(Prefix, SearchBox.Text) || StartsWith(Site, SearchBox.Text)
),
"Name",
SortOrder.Ascending
)
This formula should return all items where the Name, Prefix, or Site starts with the text entered in the search box, which would allow you to search by shorter versions of the site names.
Also, partial matching of strings within columns like "in", even using Search or StartsWith, etc. are not delegable if using SharePoint List and not Dataverse, which means it would only process the first X items, X being the data row limit. The default data row limit is 500. If you want, you may raise it to the max of 2000.

I want to make a note of the following.
Even with a delegable data source like dataverse, suppose you raise it to 2,000 and you have a data source with 20,000 records. You don't suddenly get full reign to return unlimited records. Without delegation, only the first 2,000 records are processed and filtered for your criteria. With delegation, the data source tries to process all the 20,000 records if it's delegable, however, if there are more than 2,000 records matching your criteria (suppose the 2,000th record that matches is your 17,025th record for instance), you won't get any further than 2,000. So if record # 17085 also matched the criteria and would have been the 2001th matching record, this record won't be included in your canvas app . This is because even if you have delegation, each Power Fx function does not return more than that data row limit.
So for example, if you use a Filter function, that's limited to 2,000 even if it's fully delegable. ClearCollect is limited to 2,000. And so forth.
You may be able to have a collection that's more than 2,000 records by calling Collect on it in batches. However for app performance considerations, I don't recommend keeping more than 2,000 records in memory, with even 2,000 being on the quite high side or even being too high sometimes depending on the kind of data.
For Canvas Apps in particular it's important to design your app in such a way that you use multiple Filters and intelligent design to bring your initial fetch of records below 2,000 records if and where possible.
See if it helps @Desbrina