WebP Format for Pictures with parameters

Hello
We show pictures on our homepage which contain several parameters in the file name. According to my clarifications, Cloudflare checks the extension and if it is != .jpg, for example, the image is not cached and can therefore not be converted into a WebP format.
Therefore we have set a last parameter at the end with &format=.jpg. This causes the image to be cached, but the image is still not converted into a WebP format.

Example 1 (good)
4banner_big.jpg 200 webp (Index)

Example 2 (not good)
banner2a9.jpg?context=bWFzdGVyfHJvb3R8MzI3Nzl8aW1h…jY5MmIyNzFlM2U2NTQzNTM3MDNiNGU1OTlkNg&format=.jpg 200 jpeg (Index)

Is there any way to convert images to WebP format with additional parameters?

Thanks
Roland

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