Honestly, screenshots like that full of photorealistic 3D scenery should be JPEG, unless you absolutely need to preserve every single pixel 100% accurately. (If you do need 100% pixel accuracy in a particular area, cropping out that one area is an option.)
Of course, that doesn't really answer your question of how to best (convert and) upload such screenshots. For that, there are several options:
Depending on your OS (and desktop environment), it may already come with an image format converter built in. For example, the built-in Preview application on MacOS has a "File > Export…" menu option that can save an image in a bunch of formats, including JPEG:
On Windows, plain old MS Paint can do the job, although it apparently doesn't let you choose the compression level.
One option is to download and install an image format converter. There are lots of them floating around, but one multi-platform freeware option that keeps coming up in my searches (which, admittedly, could be just good promotion and SEO) is XnConvert. I haven't personally used it, but I expect that it will probably do the job.
You could also download and install a free full-fledged image editor and use it to convert your images. GIMP is one well established option, but some people find its multi-window user interface unintuitive. For a more modern and polished choice, I would recommend trying Krita. Both are free and open source and available for Windows, MacOS and Linux. For Windows, Paint.NET (freeware, not open source) is also a popular choice. AFAIK, all of them can handle the simple job of converting PNG to JPEG just fine.
Of course, ideally, Stack Exchange would incorporate such a JS-based image format converter directly into their image upload dialog. But I'm not holding my breath for that to happen any time soon.
(It could be a possible future feature for SOUP, but to be honest, I haven't really had that much time or motivation to update it lately either. That said, I do take pull requests…)