Brightening the image may make the iso noise easier to see, but it doesn't create it.

But lossy-codecs job is to utilize psychovisual tricks to discard as much high-frequency information as possible, whilst remaining similar visual effects. If you increase the brightness in RAW and then re-encode the JPEG - more noise is being pulled up in the visual spectrum, therefor less of that information (filesize) is discarded.

For example, if you render Gaussian noise in photopea and export as JPEG 100% quality, it has 9.2MB. If you reduce the exposure by -2 it goes down to 7.8MB. That's partially because more parts of the noise are effectively black pixels, but also I believe because of the earlier mentioned effect.

Noise that's easier to see will not be compressed away by the JPEG compression. JPEG is basically just DCT + thresholding. Any higher amplitude noise is going to stay and increase the final file size.

Also, pulling more data from your 14 bit or 16 bit raws results in more noise in the end compared to the straight-out-of-camera 8 bit JPEGs.

It's not lossless