Joycon rail broke off, has been replaced but screws no longer hold it

My granddaughter somehow managed to snap off one of her joycon rails, resulting in exactly the same situation you're in. The rail screws directly into the pot metal midframe and broke off the places where the screws were secured. I ended up replacing the midframe, which is the most difficult replacement possible on a Switch, given that every other component in the entire device is mounted on it.

Here's a link to the guide I wrote: Nintendo Switch Midframe Replacement - iFixit Repair Guide

The only other possibilities I can think of would be to find some replacement screws that are longer than the originals and add nuts on the other side of the midframe. Not even sure if there's enough room back there. Otherwise it might be possible to fill in the broken mounts with something like JB Weld and drill and tap new screw holes in it. If you aren't concerned with ever being able to remove the screws again, you might be able to fill the holes with JB Weld and screw the rail back on while the epoxy is still soft. Make sure it's held together securely until the epoxy dries.