Add/Remove Software: Increasing the timeout for not asking password again?

Maybe. The thing that asks for the password is polkit. So to configure how often the password is asked, you need to configure polkit. Here are some examples of custom polkit configuration:

https://wiki.archlinux.org/title/Polkit#Bypass_password_prompt

You may also be interested in the auth_admin_keep option:

https://www.freedesktop.org/software/polkit/docs/latest/polkit.8.html