Could you please look into whether this is something which might be corrected

The bold, is a problem with the font. There is no CSS change that makes the text larger. And if you change the font-weight to normal, it's exactly the same as the text around it. The only fix I know for this would be to use a new typeface.

However the MathJax is potentially due to a configuration that changes the font size by ~124%. This in my opinion is too big. If we look at Math.SE their inline MathJax has a font increase by ~111%. And to me looks the same size as the font surrounding it. (maybe a tad larger)
I think asking for the size to be reduced is fixable and reasonable.

is a problem for multiple people on different operating systems and different browsers.

The MathJax is definitely OS and browser independent. If you are using a browser with a GUI and a JavaScript engine the MathJax should always be larger. As, as far as I can tell, JavaScript is dynamically adding font-size: 124% to the MathJax elements.

The bold font is probably OS, browser and font dependent, as it's how the system handles displaying the font. But the bold font seems to have the same height as the rest of the text and is only thicker, in all the screen shots. And so the bold is probably more a personal dislike of the font in it's font family.

I think the MathJax typeface should be kept the same, however the font-size should be reduced to something more reasonable.

We may get a new typeface that may 'fix the bold issue' if the developers agree with Use a font family which has an actual italic variant (instead of oblique). But I think the bold font is fine. It fulfills it's task well, maybe too well.
One way you could fix this is to use italics for emphasis. And bold to draw attention. (Which is how they are ment to be use, IIRC)

Could you please look into whether this is something which might be corrected

The bold, is a problem with the font. There is no CSS change that makes the text larger. And if you change the font-weight to normal, it's exactly the same as the text around it. The only fix I know for this would be to use a new typeface.

However the MathJax is potentially due to a configuration that changes the font size by ~124%. This in my opinion is too big. If we look at Math.SE their inline MathJax has a font increase by ~111%. And to me looks the same size as the font surrounding it. (maybe a tad larger)
I think asking for the size to be reduced is fixable and reasonable.

is a problem for multiple people on different operating systems and different browsers.

The MathJax is definitely OS and browser independent. If you are using a browser with a GUI and a JavaScript engine the MathJax should always be larger. As, as far as I can tell, JavaScript is dynamically adding font-size: 124% to the MathJax elements.

The bold font is probably OS, browser and font dependent, as it's how the system handles displaying the font. But the bold font seems to have the same height as the rest of the text and is only thicker, in all the screen shots. And so the bold is probably more a personal dislike of the font in it's font family.

I think the MathJax typeface should be kept the same, however the font-size should be reduced to something more reasonable.

We may get a new typeface that may 'fix the bold issue' if the developers agree with Use a font family which has an actual italic variant (instead of oblique). But I think the bold font is fine. It fulfills it's task well, maybe too well.
One way you could fix this is to use italics for emphasis. And bold to draw attention. (Which is how they are ment to be use, IIRC)