Sony provides the official update file, PS3UPDAT.PUP , directly on their support pages. You can trigger the download by visiting the official system software page:
If you see a message like “A new version of the system software is available,” you are likely on an older firmware (e.g., 4.88 or earlier). Proceed with the update. ps3 system software update 489 download link
If you're looking for even later updates, Sony has continued to support the PS3 with subsequent versions like 4.90, 4.91, 4.92, and the current 4.93, which also "improves system performance". Sony provides the official update file, PS3UPDAT
: Clicking the link will take you to Sony's official page. There, you can right-click the appropriate download link and select "Save link as..." to download the file. Do not run the file directly. If you're looking for even later updates, Sony
The PS3 4.89 Legacy: Why This Update Changed Everything for Sony’s Classic Console When Sony dropped PS3 System Software Update 4.89
Turning on 2-Step Verification (2SV) is now required. You must generate and use a Device Setup Password to sign into your PSN account on the PS3.