Are you using any workarounds or other solutions to achieve your goals in Capture One?
Having to loop around in photoshop.. which is never fun. Also looking into going via Davinci Resolve which is not even meant for photos but it has the support for it (and excellent color tools)
Doesn’t help with webp but if you are looking to compress files without further compression degradation, JPEGMini works in the here and now.
JPEGMini does not help when clients request webp, which I remember having seen here:
https://support.captureone.com/hc/en-us/community/posts/12358932414493-Add-AVIF-and-WebP-export
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Consider searching for existing requests and upvoting them, it could be beneficial if single request have more weight than having scattered small-weight requests (or upvote them in addition to yours).
Check out JPEGMini.