But seriously: how do I change the frame rate of a frame animation?

To add to the other very good answers:

The animated GIF format does not have a frame rate that works the same way as a video frame rate. That’s why you see a Frame Rate option only when the Timeline panel is set to Video mode, and not in Frame Animation mode.

Animated GIF allows each frame to have a different delay time, which is quite unlike the typically uniform frame rate of video. If you want a specific delay time between frames, you can of course set that in the Timeline as already shown. Another way animated GIF is different than video is that if you don’t specify a delay time, most animated GIF players (web browsers, etc.) will simply play back all frames as quickly as the computer allows. Which means the same animated GIF could play back at different speeds on different computers.

Because of all of the above, it’s correct that there is no frame rate option in Save for Web (Legacy) for animated GIF export. Save for Web simply applies whatever frame delay you used in the Timeline panel because the animated GIF format doesn’t provide for a video-style frame rate. And the way that format works is of course is outside the control of Adobe.

Hi @Jon269864278sog In addition to the great explanation from @Myra Ferguson on using the video timeline, here are some screenshots that might be helpful in adjusting the frame rate when you want to output an animated GIF in Photoshop. Here, it's called setting a frame “delay” instead of a frame rate. Click the little down arrow below each frame where the seconds are shown. That brings up a menu with some preset times, or choose Other... and set your own delay time (up to 240.00).

When you create a frame-based animation, you can set the duration of each frame by changing the time underneath each frame in the Timeline. You can also convert your frame-based animation to a video timeline where you can set the frame rate. To switch to a video timeline, go to the Timeline panel menu (the hamburger menu in the upper right of the Timeline panel) and select Convert to Video Timeline.  Once you have a video timeline, go back to the Timeline panel menu and select Set Timeline Frame Rate...