Knees are why I cycle.
Not precisely protein. If I am right about how much energy you could get from fat, and assuming glycogen isn’t sufficient to make up the arrears, then you used amino acids from your labile pool. The labile pool is a buffer for amino acids which by weight comprises roughly 1% of your total lean mass. Those amino acids are potentially going to be used to make proteins only if you don’t need them for energy.
That buffer is filled by your cells recycling proteins excess to requirements, or digestion of dietary protein, and emptied by your cells making new proteins (and other molecules based on amino acids), or using them for energy.
Sure if you use a lot for energy persistently and don’t refill them you may inhibit the production of new proteins and because we’re continually tearing down and rebuilding proteins you could be losing muscles for a fast at that point.
Same - knees are why I cycle.