What is the ruling on using someone's personal belongings without their permission, knowing that they would agree to it?

The basic principle is the prohibition of benefiting from another's property except with their willing consent, as the Prophet (peace and blessings be upon him) said: "The property of a Muslim is not lawful except with his willing consent."

If a person's consent for the use of their belongings is known, then there is no harm at that time, based on the aforementioned narrations and Allah's saying: ﴿There is no blame upon the blind, nor any blame upon the lame, nor any blame upon the sick, nor upon yourselves, if you eat from your houses or the houses of your fathers or the houses of your mothers or the houses of your brothers or the houses of your sisters or the houses of your paternal uncles or the houses of your paternal aunts or the houses of your maternal uncles or the houses of your maternal aunts or that which you possess keys to or [from the house of] your friend﴾. This is all provided that the eater does not take it surreptitiously (khubnah), does not intend thereby to protect his own wealth, and that the item is insignificant and minor.

Therefore, if you know that these people consent to your use of their belongings, there is no harm in using them without their explicit permission, due to the presence of customary permission.