Scifi recommendations

The Mote in God’s Eye is hardly recent.I don’t know your tastes, but if modern:Space Opera is your thing you could try the late Ian M Banks Culture series (start with The Player of Games, even though Consider Phlebas was published first and is chronologically first).Alistair Reynolds’s Revelation Space is worth a look.So is Anne Leckie’s Imperial Raadch series, starting with Ancilliary JusticeIf you want something (much) more down to Earth, the alternate history space program in Robinette Kowal’s The Calculating Stars might appeal. (It won the Hugo for best novel this year - presented by Jeanette Epps - very appropriate).If you are prepared to put up with fantastic elements in your SF, then N. K. Jemisin’s Broken Earth trilogy or Yoon Ha Lee’s Machineries of Empire series might be worth trying (for the latter read The Battle of Candle Arc first - as a taster and because it introduces some of the weirder stuff}

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The great classics rarely are, by definition. Publication date is not a concern.

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I don’t think that The Mote in God’s Eye is a great classic in that sense. It was a work of its time and - in SF - a major work in its time. But things change.For real classics I’d go to Stapledon for First and Last Men or Wells for War of the Worlds and The Time Machine.
Or some of Ursula le Guin’s SF - The Dispossesed is considered a classic.For influential works I’d go for E. E. Smith’s pulpy Lensman series (skip Triplanetary for sure and probably First Lensman too). Maybe the original Foundation trilogy, too (although I haven’t reread it at all recently and I was greatly disappointed by a reread of Asimov’s robot stories).

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...in recent years his son Brian Herbert and Kevin J. Anderson have written a series that back stories to the Dune books that I enjoyed.

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I have...heard of those.

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I also like Neal Stephenson's books, especially Seveneves

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I think that Anathem is pretty good. The Rise And Fall of D.O.D.O. is fun.

There’s a reason I pointed to them as influential, rather than good.But Donald Kingsbury wrote a rather good unauthorised sequel Psychohistorical Crisis with numerous changes of names.

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I remember really enjoying Dune - are the sequels worth delving into?

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Dune Messiah is good. Children of Dune completes the original trilogy. The sequels written by Frank Herbert are interesting enough I won’t tell you not to read them, but don’t expect them to match the originals. If you can get through
God Emperor of Dune you may as well read the rest.As for the additions by Brian Herbert and Kevin J. Anderson I refer you to my previous answer.