BNYM Stock IDX IS for 401k contributions

I recently changed jobs, and my new employer's 401k is through Fidelity. I've always used Vanguard, but I understand that Fidelity has some good options for index funds. In my Vanguard accounts, I am either invested in the total stock market index or the S&P 500 index, as I am 32 and plan on letting this money ride for a while.

My new employer's plan does not offer what I thought were the "traditional" Fidelity equivalents of the two Vanguard funds that I use. It does, however, offer BNY Mellon Stock Index Fund Institutional Class, which tracks the S&P 500.

Does anyone have any familiarity with this fund? It appears to do the same thing as the corresponding Vanguard fund. I'm not familiar with it, but is that only because it is fairly new? Bank of New York is presumably a reputable institution, so it seems legitimate. Also, the expense ratio is 0.02%, which I like.

I also have the option of opening a brokerage link account. Is it worth doing so if I only want to open the account to access Fidelity's other total stock index funds? I'm a set it and forget it investor, will the BNY fund be sufficient?

TIA and