How hot can a lithium ion battery safely get while charging?
There is not good/bad, probably that 113 F (45 C) is probably on the conservative and safe side.

Being able to charge a phone quickly is a selling point so Samsung probably deliberately allows for a higher temperature before the charging rate is decreased.

A higher temperature decreases the lifetime of the battery.

Samsung choose their optimum balance between battery charging time, safety and lifetime.

Your choice might be different dependent on the application. If a long charging time is not an issue then that 113 F is probably fine.

And as mentioned in the comments: read the datasheet