I think you can probably credit Sanders for Medicare For All being such a big thing right now. But, rhetoric aside, Biden was always going to be proposing to expand on Obamacare and add a public option. Like, that's not actually a leftward move from Obama -- that's what Obama wanted to do in the first place. And surely someone would be running to his left.
And then obviously Sanders doesn't get any credit for the party's moves leftward on anything other than economics.
I think how much credit you give him for things like student loan forgiveness, support for unions, and various schemes for taxing the rich depends on to what extent you see him as responsible for the rise of progressivism. I think a problem for the idea that Sanders '16 made this happen is that Occupy Wall Street was 2011. Obviously this stuff is very hard to disentangle but I feel like I'd give more weight to the global financial crisis and the internet, which respectively produced an overeducated/underemployed activist class and gave them the means to organize. And, like, we know that the large majority of Sanders' supporters in 2016 (and a significant share even now) weren't really with him because of his ideology so I don't know that I buy that he did much persuading or that the party has moved left to retain the support of his voters.
I think another factor in the rise of the left is the rise of the idea that "electability" isn't real or at least isn't important, and that you win by turning out your base. I think this started as a response to seeing Republicans do so well while moving so far to the right under Obama. But by the 2016 election this had taken hold in entirely Sanders-independent ways. Hillary was way more outspoken on racial injustice than any previous Democratic nominee (and I'd bet quite a bit that she'll still be the record-holder after 2020) and way more outspoken about the pathologies of the Republican base ("basket of deplorables"). She felt a lot of pressure to do this kind of thing because activists on the left felt unconstrained by concerns about electability, either because they believed that base turnout was more important or because they believed that Republicans had already been demographically doomed and Trump had no chance. In retrospect this was wrong, and probably she'd have done better had she not seemed so threatening to white conservatives, but many people took the opposite lesson from this and decided that Hillary was too moderate, and have doubled down on the idea that you win by turning out the base.
So far in this primary, we saw everyone initially racing to the left before recalibrating as they realized that they were actually to the left of the median Democrat on a few issues. I think now things have settled down and there's a more nuanced understanding of the political landscape. Now we're back to chasing the center, but we're chasing the center with ideas that are supposedly leftist, like large, universal expansions of the welfare state and raising taxes on the rich. This isn't so much the party giving way to its left wing as it is the party realizing that these are popular positions in the country as a whole, and overwhelmingly popular positions among Democrats. At the same time we've seen a move away from the progressive positions on racial justice and to some extent on immigration (though this is complicated because everyone wants to draw a contrast with Trump), because these aren't actually that popular. But it's not as simple as "left on economics, right on social issues" because at least some of the left wing positions on social issues are political winners, at least among Democrats, like gun control.
