As Fixx said, the menu options for rotate left & right only affect the view of the canvas, not its actual rotation. As with everything else in a menu, you can set shortcuts for these items (Preferences > Keyboard Shortcuts > Develop > View). There is also a preference in the Tools section to enable canvas rotation with a trackpad (may be Mac only/).
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Initially there was buttons to rotate the image in Develop Persona but we had to remove them later due to some issues.
I believe they will be added back as soon as we find a solution for this.
Seems you cannot rotate properly in Develop persona. You have to develop image first, then go to menu Document>Rotate 90°..
(I hope Affinity would not use too many toolbar/button strip buttons; they are hard to find, not really macintoshy, would prefer menu commands, contextual menu and panels.)
AP generally reads camera orientation data just fine, there are just some camera model's raw which is problematic. Anyway, sometimes you want to rotate image anyway as you have shot in angle and want to use image angled just differently. So rotate in develop is a must feature.