as recommended by most YouTube videos I've seen
Ouch. It would be best if you found better Youtube channels. :)
You need to differentiate 4 types of files.
I. Source files.
The native file format where you are producing the files. And here we need also to differentiate the correct application for the work. In this case vector format; Illustrator, Corel Draw, Affinity Design, or even Inkscape.
I make different versions of the source logo files, for example with the original fonts, with strokes of different widths or objects intersecting the logo. You do not deliver those to the client.
II. Delivery files
In the case of a logo, the files should remain as vectors.
If the main goal is going to be printed in a commercial printer, or let's say the file is part of identity guidelines, the colors should be defined for example in Pantone, and the file format should support it. This reduces the options to PDF, and could exclude using SVG as it uses RGB.
Keep in mind that there are many flavors of PDF. PDF is not a "Save it format", it is an "Export it format". So you need to export it correctly.
You can also provide a native file format, but without any effects, overlays, layers, etc. Avoid even strokes with width. A simple plain, clean Logo on curves. No intersections, embedded fonts, or anything like that.
More could be said about the "original logo". You normally deliver it in the document with some context, a basic identity manual with annotations like the different colors allowed.
III. Supporting or complementary files
Not every client knows how to extract the vectors of a PDF file (but the design department should). So, in this case, you can provide additional files like a transparent PNG, but only as a "courtesy" to simplify the usage on Office software, or social network apps like Canva.
SVG file format is something in between. It is a vector file, that could be used as an original, but as is the logo naked and in RGB only it is not ideal for "the original" for branding. If the branding is electronic usage only, it could be one of the delivery formats.
IV. Applied files
You can provide the logo implemented in such applications, for example, a Word or PowerPoint template, with a well-defined resolution in case you need to implement it as a raster image.
The problem is that you provided a file type III, which is not ideal as the main source, and the client probably made additional strawberry jam or mashed potatoes with it.