Image size different in 3 different places

No because there isn't one until you save it.

And what Camera Raw shows you is not the file size, but the total number of pixels in the image (the pixel count).

This is expressed in megapixels (millions of pixels) - MP.

Your image is 2512 by 2512 pixels. which equals 6.3 million pixels.

This is all perfectly normal.

The jpeg format uses very aggressive data compression to reduce file size. It can squeeze a file down to 2% or 5% of original size. But at the price of permanently degrading the file.

However, the file doesn't become a jpeg until it is actually saved to disk. It's an encoding process as you save. When the jpeg is open in Photoshop it's just a pixel array like any other file format. It's not a jpeg when open, it has been decoded and the size blows up again.

A raw file is yet again a completely different thing. It's not compressed, but it is a grayscale image without color information. It has only one channel. So merely processing it into an RGB file triples the file size - in addition to many other technical aspects like bit depth and so on.

There are many different ways to count the size of an image. The file size is only one. Other things include memory needed in total, and the memory used to hold a flattened uncompressed image.

Bridge deals with files on disk, so it can show you the file size.

Photoshop cannot know the file size until it is saved (and it depends how you save it and what settings you use). So you cannot get this information except by trying out saving with different settings. There is no magic solution to reach a target size.