While official EBOOTs can be purchased and downloaded from the PlayStation Store, "collections" found on community sites like Playstation ParadiZe
Sony officially sold PS1 Classics on the PSP and Vita store. You can still download these if you own a Vita and have a PSN account.
When you see a user sharing a "Complete PSX EBOOT Collection," they are sharing libraries of these .pbp files, usually organized by genre, region, or letter of the alphabet.
A collection of 1,300 games sounds impressive, but 900 of them might be Japanese Mahjong simulators or sports titles from 1996. The best collections are curated by genre or by "All-Time Greats." A "Complete NTSC-U" collection (North America) is the gold standard for English speakers.
PS1 games remain copyrighted by their publishers (Sony, Square Enix, Konami, etc.). Distributing EBOOT collections without owning original discs violates copyright law in most jurisdictions.
Unlike standard emulation, the PSP and Vita use a native "POPS" (PlayStation On Portable System) interpreter, which provides high accuracy and performance because the hardware is architecturally similar to the original PS1.