No, it is not possible.
A SVG file loaded thorugh the <img> element is treated as an external resource, like any other image format, so you can't use CSS or JavaScript from the HTML document to manipulate its content.
https://stackoverflow.com/a/22253046
https://css-tricks.com/using-svg/#the-problem-with-both-img-and-background-image
Of course you could play with CSS filters to change its color as you could with another image format loaded through the <img> tag. This actually changes the rendering of the <img> element not its loaded content.
You can also apply a <style> tag in the SVG document itself to style it directly. Or add attributes to SVG's elements you want to change appearance. The this styles would be loaded when using it as an external image from <img>. But both options require changing the SVG file itself and using raw CSS and SVG attributes instead of tailwind.
If you want to style your SVG using the same CSS/Tailwind avaiable in your HTML document use it inline.