Can I install iOS 26 on my iPhone 13?

You are told to not install it on a primary device that is needed for daily use. You should expect many things to not work correctly and you may experience complete data loss if you do not follow the instructions closely, when attempting to remove the beta. You will not be able to remove the beta unless you have a computer. There is no support for beta software, so you are on your own as a tester with the only option to report any issues using Feedback Assistant.

To Beta or Not to Beta - That is the Ques… - Apple Community

It's a beta. There are LOTS of "issues" with it. Betas are intended for testing, not for real world use.

Can I install ios 26 public beta in my new iPhone 13.Is there any issue with it.

Can you?......Yes.

Should you?.....No.....unless you have a spare phone to install the beta software.

Wise decision.