It is a fascinating topic. The Sun's age is determined on the H-R star diagram today based upon the radiometric ages of various meteorites that determine the starting point for what is known as the Faint Young Sun or when it was zero age main sequence or ZAMS. The Sun's present position on the H-R star diagram is very different from where it started some 4.6E+9 years ago according to stellar evolution models developed using the radiometric ages of meteorites. Clair Patterson fixed the age of the Earth and solar system in the mid-1950s using meteorites. This is the basis for all calculations that followed for the age of the Sun and solar system used today. The spin rate of the early Sun could be >=16 km/s at its equator, today it is closer to 2 km/s. The spin down age for the Sun's rotation cannot be directly measured by telescopes so is interpreted within the meteorite age dating model and other comparisons with stars and their spin rates as well as H-R ages used. All H-R star diagram ages calculated must start at an initial p-p (proton-proton) chain fusion point on the diagram called zero age main sequence or ZAMS. This critical starting point varies for stars of different masses. Documenting ZAMS stars and ZAMS clusters today is challenging to show on the H-R star diagram.
FYI, here is another important note I feel on how stars are dated. "The evolutionary track that a stellar model traces in an HR diagram is somewhat code dependent. Many stellar evolution codes are currently being used, and they produce different results in part due to uncertainties in the input physics (such as the opacity, the equation of state, and the nuclear reaction rates),…", Ref - p. 511, Allen's Astrophyscial Quantities, Fourth Edition, 2000. My note. The ZAMS equation of state and nuclear reaction rates for the Sun were fixed using radiometric age of meteorites in mid-1950s when Clair Patterson studies fixed the age of the Earth, Sun, and solar system. This ZAMS plot for the Sun is used to model the Faint Young Sun and other star clusters HR plots too.
FYI, here is some more information on how the Sun is dated, from a source that sent me this information.
"We can compute a ZAMS for a given composition, however, the computed ZAMS is highly model dependent to the extent that this hardly is an exact science. If it were an exact science, one could compute the ZAMS for solar composition and then determine how far above the ZAMS the sun is and from that compute the sun's age. One certainly gets this impression from most textbook discussions of this topic, but this isn't done. Rather, in computing the sun's initial position on the ZAMS, it is assumed that the sun is 4.6 billion years old (based on meteorite ages) and hence its initial position is computed downward from the sun's current position on the basis of the assumption of 4.6 billion years' worth of nucleosynthesis in its core."
My note, the Kelvin-Helmholtz equations result in a much younger Sun but the meteorite age is the standard.