Regarding the New Labour project, yes it was a modernisation of Labour.
The smart thing was they recognised the world had moved on from traditional socialism. The ideological arguments had been had and the socialists had lost, so they didn't try to undo the work of the previous Tory governments.
Blair said: "OK, I still hold core Labour values of social justice and a consider myself a progressive, but I'll build on top of what the Tories did rather than try to unwind it." So he was OK with companies and people being individually successful and wasn't antagonistic toward Business, as he was depending on those successes to fund his social programmes. The "Third Way" as he put it. That was a very appealing message.
Contrast that to some of the regressive nonsense in the 2019 manifesto; reading stuff like wanting impose identity politics on any company over 250 employees would, in practice simply have limited any mid sized company to never bothering to try growing over 250 employees. How does that sort of antagonism create a successful and dynamic economy?
History shows that the more rigid a set of legislature becomes, the more brainpower is dedicated to finding a workaround to that framework. But then if any of the Labour front bench ever had proper jobs in the real world, or better, run a business and created jobs, they would not be so blind to this.