I've always thought that Wimbledon is her best chance of winning another major these days. There has been a bit of talk about her skipping RG this year, and playing a grass court tune-up event before Wimbledon. We'll see though. As others have said, she is still continually reaching the latter rounds of majors (recently beating the world no. 7 and world no. 2 in Melbourne) and isn't bombing out in the 1st week or anything, so I wouldn't write her off just yet and she should still be optimistic about her chances of winning another major.
I personally have never thought that Serena needed to surpass Court's record to become the greatest, especially given that she has won her majors initially from 1999 and during the 00s which was a golden era for women's tennis with stacked WTA top 10s, and during the past decade when the overall strength in depth of the WTA top 100 (and beyond) has been vastly superior to that in the 70s, 80s, 90s etc., when there was very little depth outside the WTA top 10 (or even outside the top 5 in some cases). It's a completely different scenario compared to men's tennis, in which there has always been a lot of depth throughout the open era. I certainly do not think that there is greater depth (at least in the top 100) in men's tennis in 2021 compared to 1991 for example, while in women's tennis there blatantly is and by a huge margin.
I will say though that it's a myth that Court's record wasn't talked about in previous eras. I'm pretty sure it was regularly mentioned when Navratilova, Graf etc. were dominating. I remember talk in 1996 when Graf moved from 18 majors to 21, about whether she could surpass the record. Of course the 'Australian Open context' was also mentioned at the time as well, and I don't remember much talk about Graf 'needing' to surpass it to establish herself as the greatest, but it certainly wasn't ignored or dismissed as completely irrelevant. Graf winning RG in 1996 to surpass Evert and Navratilova in the majors count was a big deal (Evert was publicly and privately gracious, while Navratilova was incredibly bitter - go figure), but no-one talked about her setting an 'open era record'.