Why is my PSD file smaller than the previous graphics designers PSD?

I do know that the actual pixel size doesn't matter when it comes to television broadcast, since it's set to the dimensions of the screen (1920x1080), but I do know that things will quite often get repurposed for other promotional materials. Quite often, things were designed for the screen first, then those elements were taken to pull out pieces for print and web. That's why we worked in 300ppi. But if where you are working has zero plans to do anything like that, then it doesn't matter at all.

Worked for two decades in television as an editor and designer. For one, the other designer may have been working at 300dpi, which many designers still do for the most part for high end television stuff, like HD and larger. That alone could make a difference. Also, you may have a different technique as to how you put things together. They may have kept a lot of stuff in their files for possible revisions, which are very very very common in television. So if you are designing something, and they want changes, keep the old versions as well because quite often after all of the changes are made, you have ended up pretty much right where you started from. I know a few designers I worked with that had huge files like you are talking about just for that reason. Some files had 5 or 6 versions built in the same file. Makes for a big fie, but also made life a lot easier when it was crunch time and revisions were asked for.

Only jpegs sacrifice picture quality to reduce file size. That's lossy compression. Photoshop, Png and Tiff can use compression to reduce file size, but there is no sacrifice in quality. That's lossless compression.

There are many reasons a file can be larger than expected. Layers increase file size, but there is another factor called "Document Ancestors", metadata imported into a file with other elements.

I don't know the specifics of the original file, but quality-wise, no worries.