I’m currently using lossless WebP, but as I see it, I will probably need to make changes to control the file sizes in the future.
While lossless webp might be better than png, it still is a format to preserve pixels. It is for pixel art. You did not create your artworks with pixel accuracy in mind. Using this format means, you preserve the dithering your rendering software used to create natural looking surfaces. If you use a "lossy" format, it compresses those surfaces into math that will recreate a natural looking surface. Texture. Whatever you call it.
You can go down pretty low on the quality factor for testing. It will break down when you see squares and the hard lines get fuzzy.
Even a placebo setting of 100 with lossy webp will get you much. Your screenshot with the red bikini is 2.91MB in png. In placebo setting lossless it is 1.6MB which is impressive. But in lossy placebo 100 webp it is only 411 kB. In default 75 in mode slowest it is 82kb.