Is There an Ongoing Debate about the Impact of Solar Variability on Climate?

This is part 1 of review of the claims in Connolly et al 2021. You can see part 2 here . A paper was published in 2021 arguing that scientists have been premature to rule out the possibility that the Sun is the dominant explanation for the current warming trend. One key element in this argument is that there is continued disagreement over the degree of solar variability in reconstructions of Total Solar Irradiance (TSI) since 1610. Some reconstructions show "low solar variability," and if those are correct, then current warming may be best explained by anthropogenic forcings. However, if "high solar variability" reconstructions are correct, then solar variability may explain most of current warming. So Connolly et al argue that "the answer to our question 'How much has the Sun influenced Northern Hemisphere temperature trends?' depends substantially on which estimate of TSI we choose."[1] But is this correct? Connolly et al Figure 2 Figure 2 in h...