But how would you go about checking if the TIFF file is indeed uncompressed?
A quick test.
Open your photo, and re-save it as TIF with another name, with no compression. Compare the file weight.
The file size of an uncompressed image will be about the same.
I'm worried it could just be a lossless container for a lossy photo.
It is a very specific case. It is not about compression, as your first inquiry, it is about lossy compression.
Make some additional tests with different compression methods. LZW or ZIP (both lossless)
If the file size is a lot smaller than those, it was probably saved using JPG compression, therefore lossy.
But the one and only exact test you can make is taking the original photo, overlay it using "difference" as blending mode, flatten it, and see the histogram. https://otake.com.mx/Apuntes/Imagen/PruebasDeCompresion/1-CompresionJpgProceso.phtm
But take into account that there is a big chance, the original photo was saved as JPG from start.
And yes, TIF format is very specific. I would not recommend it for normal photographers. I only would recommend it for specific cases:
When you need a 16 bits per channel image and you can not send a PSD file.
When you are saving a CMYK image, you do not want to use JPG and cannot send a PSD file.
Some weird file, like a multi-channel file, CMYK and transparency, etc... and you can not send a PSD file.
And that is probably it.