Fist let me ask you to not be angry and rude to people who are trying to help you. All are just doing this as a hobby, in their own spare time. Nobody is getting paid to help you, not did anyone get paid to produce Coppermine. It is a free package produced by many people, again as a hobby, over many years. You will notice this site doesn’t even have advertisements, meaning there is zero revenue for anyone in the team. Please try and be polite.
Which part of the docs do you find rude? Pleas remember, many parts of the docs are written by non native English speakers. So while you may see them in your head as rude, you need to understand how they were written and translated.
So back you your problem. I had to jump through hoops to test your images as your settings mean the full size images (the ones that should contain the EXIF) require a logon to see. So to get to see them I had to come off my iPad to a PC, manipulate the output image links so I can download and check them.
So the first image, from a Powershot A75 with 3mo sensor. So output images are 2048*1536
The full size image is at those dimensions, so has not been modified suggesting it has not been modified on the server. Any modifications using GD on the server remove EXIF data, a limitation of GD.
The second image, which you suggest is from a Rebel XTI or Canon 400D as it is known here in the UK has a 10mp sensor so the full-size resulting image it outputs should be 3888*2952 pixels.
However, the image you link to is obviously not that resolution. It had been manipulated either before you uploaded it and cropped to 1734*1322 (which is what I suspect given the aspect ration and low resolution image) or you have edited in Coppermine, or it was larger than the settings you have allowed (File size or max width dimensions set in config) so the script on the server has modified the file to comply with your settings. So either EXIF has been removed by your pre upload edit, or by the server during upload as it had to resize.
Given your image, and the fact you have not provided an account on your setup to test, and an unedited image for us to test it is not easy for us to help. Provide those and it may be easier.
I did however dig out an old Canon 400D and tested on my test setup. Once I had setup my install to allow the full resolution and file size in config all the EXIF remains, as it should. I also tested with my Canon R5 with its silly big files, and the EXIF works.