I am still trying to develop a clear idea myself. This summarises where I have got to in my researches (from respected piano technique books and some YouTube piano teachers plus a laws-of-physics/engineering mind). Mine is an amalgam of views that made sense to me.
I think the finger strength idea comes from the finger independence school of piano techniques. The premise is: to play precisely you need to control the velocity of the key down action precisely. So, playing a legato passage very quietly requires each key to launch the hammer at the strings so that each hammer touches delicately and the key arrives at the key bed before releasing the key to apply the key damper.
Having strong playing fingers while being able to relax muscles in arm, shoulder, back and in the lower arm for non-playing fingers yields more control - once you get the hang of it. Weak fingers are likely to have less control so will recruit compensating actions from muscles in the wrist, arm weight and back. In one book I use, the author says some piano players were said to have fingers of steel. (I think that was Horowitz - I might be wrong). That strength would allow them to play fast pp and ppp passages evenly with ease. I think they must use their fingers to press down the keys more than they use wrist flexibility, rotation and arm weight.
Next comes the matter of equalising the finger strength across the hand vs. choosing the fingering to take advantage of the different qualities of each finger. You will find lots of exercises that focus on developing fingers 4 and 5. Mine are weak so I do these exercises from time to time. Presently, I doubt going overboard with finger equalisation exercises will do me any good. One reference book I use says develop finger strength but don't expect equalisation, so choose your fingering accordingly.
To put this in contrast, Dorothy Taubman developed a different approach. She looked at child prodigies who at a young age were playing very advanced pieces very well. Their fingers were not strong, so how did they play so well? It appears they used arm rotation actions, wrist flexibility and arm weight to a greater extent. These techniques offered control but in a different way. The Taubman techniques are not just about rotation, but it features.
Some piano technique experts argue that one is better than the other. There are some strong opinions on this from highly skilled pianists. As far as I can see, both pedagogies have merit and can be used together.