What a scanned PDF really contains
A scanned PDF is a container holding one image per page. There are no characters in the file, which is why search returns nothing and copy returns nothing.
Adding a text layer through recognition makes the file searchable while leaving the page image visible, so it still looks like the original.
Making it searchable
Run recognition over the whole document and save the result as a searchable PDF rather than as plain text if you need to retain the page images.
Search will then be as accurate as the recognition was. Faint pages will have gaps, so do not treat a zero-result search as proof a term is absent.
Managing file size
Scanned PDFs are large because they store full page images. Greyscale instead of colour typically cuts size by two thirds with no loss for text.
Compress with care. Aggressive image compression is the most common reason a previously readable archive becomes unreadable a year later.
Keep an uncompressed master copy if the documents matter, and distribute the compressed version.
Splitting, merging and reordering
Split long scans into logical documents before recognition so each output file is meaningful on its own.
When merging scans from different sources, normalise page size and orientation first, otherwise the combined file is awkward to read and print.