The twin paradox is about breaking the symmetry. If a third observer moves at the same speed, but the opposite velocity, the third observer adds a third coordinate system and the symmetry is broken. Thus when the third observer comes back and meets the original twin, the sum of the twin out until the meeting of the third observer+the time back from the third observer, the sum of the time lengths will be shorter. If and only if, there is a break of the symmetry, does the time distance become measurable in “proper time.”

Sorry, you don’t get it. Each person in relative motion is in their co-moving reference frame. This has only a time component, no spacial movement. Their internal time goes at their usual time ticks, regarless of their relative motion. So, their lives are of usual length. If either of us, measure in our clocks, the other person’s clocks, they each will measure the other at slower tic tocs. Their internal clock rate can be measured via the “proper time” c^2 tau^2=(c Delta t)^2-(Delta x)-(Delta y)^2-(Delta y)^2-(Delta z)^2. Measured in proper time, the elapsed time in either clock is the same as both of our internal clocks. This is Minkowskis measure of 4-dim space-time that is the same for every and all observers.

There is an invariant of SR, called the “proper time, tau.” In your co-moving inertial frame, this is the same as your local (biological) time. As an invariant EVERY observer can compute it in their frame relative to yours. For a different inertial observer, they compute this by taking two locations including time, i.e. (t2,x2,y2,z2) and (t1,x1,y1,z1). Then c^2 tau^2=c^2(t2-t1)^2-((x2-x1)^2+(z2-z1)^2+(z2-z1)^2). This quantity is the same for all observer, regardless of their relative inertial motion. In this sense THERE is a measurement that everyone agrees on, just not x,y,z,t that Newton assumed. In x,y,z,t measurements, all the SR effects show up. I don’t think I would call it simultaneous but invariant.