@unlink Monterey has some indexing issues which can cause issues for Alfred's file search, especially the earlier 12.0.1 version you're on.
As a workaround, try changing Alfred's default search scope to everything. Open Alfred's Preferences to the Features > Default Results, and untick macOS Applications Folder and Folders in Home. Then remove all folders listed, and add in your Macintosh HD. Your prefs will look like this:
Now try searching for files using Alfred's file search mode. Show Alfred, press the spacebar, then type a filename. For example:
[spacebar]desktop
For a proper fix on Monterey, refer to @Vero's post here, taking particular note of giving Terminal access to delete the .Spotlight-V100 folder: