Affinity Photo does not have the beloved Photoshop Crop to Selection feature. This should be an EASY tool to implement in their software.
BUT, there is a workaround that I use all the time...not that I'm making excuses for Affinity Photo.
1. Make sure image is rasterized first.
2. Make your selection using any selection tool.
3. Copy / Ctrl+C
4. Click "File" > "New From Clipboard"
This will open a new window with only the selected portion of the image. The original image will remain undamaged.
If you don't need the original image, then discard it.
I know, annoying, sometimes I don't care if the original image is damaged because I only need a small snippet of the image, but this is the only way I have found that works for me.
After performing the actions above, I copy the image from the new window created via File > New From Clipboard, and paste into my project.
Not sure if this is what you're looking for or not, but hope it helps either way in some form or another.
We all want a practical 1-step Crop To Selection Tool...which is why this thread is so MASSIVE!