This question is more frequent than imagined.
It is assumed that resistors or electronic components connected to the same two nodes have the same potential difference. It may seem obvious. But why does this happen? Let's prove the obvious! :)
The question then changes to: why connecting components (for example R1, R2 and R3) to two nodes A and B through a perfect and ideal conductor means bringing the potential of point A and point B to these components?
These doubts are due to the way in which certain quantities are explained (the electrons that "have" a potential energy) compared to the fact that we lose focus on what these quantities are.
Let's tkink crazy! We reason by absurdity.
If the potentials were perhaps different, for example in the electrons "outgoing" from the resistors, we would each have them with a certain "electric potential energy" still to be "spent" and in a different quantity for each branch converging towards B in which they are found.
We also know that on the conductors carried by current there are surface charges that generate the electric field useful inside them to push the electrons against the resistivity: in perfect conductors this resistivity is zero so the electric field will not be generated; in fact, the surface charges will naturally arrange themselves so as not to have an electric field (and potential difference) along the path. However, this also means allowing the surface charges placed on the three branches to arrange themselves so as not to have a net electric field in any part of the (perfect) conductor: the currents will pass but there will be no energy expenditure and the potential (energy to be spent) will thus be the same for all the electrons contained in each of the branches.
Therefore, connecting the components in parallel to two nodes A and B does not mean "bringing" the potential of A and B to the components, but "making the potential of A and B equal" for all components thus connected.
In addition to the microscopic form of Ohm's Law it may be useful to examine the matter with Kirchhoff's laws, especially the law of voltages based on the principle of conservation of energy within a closed path.
A circuit is a system, it adjusts itself.