Starting over. We've all been covering a lot of ground without relating nearly any of it to what you're doing. We aren't going to get anywhere this way.
I looked at tutorials that show how to go into DISPLAY and unclick something, but my Mac does not offer that option.
Not enough information. Unclick what? If you mean Automatically adjust brightness, then per your screen shot, it's already off. Which it absolutely must be for color management. And that means not even moving the computer from where you normally do your color work. You should be doing such work in a space that has neutral lighting that never changes.
Why should automatic brightness be off? Because a monitor profile is made by first setting the calibration. This is the white point, black point, gamma curve and gain. Once those are set, a profiling package then reads a series of color patches to measure the gamut and color range of your monitor. Since the color of those patches are affected by the calibration, you CANNOT change any calibration settings after the profile is created, or that profile is instantly invalid.
one cannot get rid of the "glass" effect, which I suspect is the problem.
The new GUI look has nothing to do with this. Not even a little.
Now to the meat of the issue. What is causing the color shift going from Photos to Mail? On a personal note, after doing some testing in Photos, this is why I don't, and will NEVER use the app.
When you do an export, these are the default settings:

The Color Profile drop down is a huge red flag! What is that? Why is an unknown space the default? So, I tried it to find out. Apple (sort of) converts the exported image to a profile named Apple Wide Color Sharing Profile, which it embeds. When I compare the original and the exported image, the one Apple converted to this secret profile is indeed darker than the original. Which right away means it's doing a lousy job of converting the color.
So then I wondered, what is Apple Wide Color Sharing Profile? Basically, it's a nearly 100% copy of Display P3. You can display the two in comparison mode in the ColorSync Utility to see that. Which then begs the question, why have Most Compatible as a choice at all? Just make the default Display P3, which is one of the other choices.
Try this as a first test. Export an image and make sure to choose Original, as shown next:

Drop that exported image into Mail. Does it now match what you see in Photos?