The 25 V capacitors are unlikely to have been damaged by a 24 V supply, even if it was actually at a slightly higher voltage.
Is the 24 V supply the same polarity as the 12 V one? Are + and - in the same place. There is a diode (D1) to protect against damage if the polarity is wrong, but it would be worth checking that diode.
One of the 8-pin integrated circuits is a buck regulator, an APW8720B.
https://pdf1.alldatasheet.com/datasheet-pdf/view/548591/ANPEC/APW8720B.html
That is what is most likely to have been damaged, because it is only rated to 16 V.
You could try finding a replacement. You will need a hot air gun to unsolder it, because it has a metal pad under the IC and those are just about impossible to solder with a soldering iron.
You could also try providing the power from another power supply. If you can measure the resistances of R14 and R10, the output voltage can be calculated.
View attachment 133146
The output voltage will be 5 V or less, because the other electrolytic capacitors are rated at 6.3 V. However, it would not be safe to assume that it is 5 V, because it could be 3.3 V or less, and 5 V would cause damage.
When you find the voltage, if you supply power to the + and - of the 6.3 V electrolytic, the router might work.