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We Are Legion (We Are Bob)
Bob Johansson has just sold his software company and is looking forward to a life of leisure. There are places to go, books to read, and movies to watch. So it's a little unfair when he gets himself killed crossing the street.
Bob wakes up a century later to find that corpsicles have been declared to be without rights, and he is now the property of the state. He has been uploaded into computer hardware and is slated to be the controlling AI in an interstellar probe looking for habitable planets. The stakes are high: no less than the first claim to entire worlds. If he declines the honor, he'll be switched off, and they'll try again with someone else. If he accepts, he becomes a prime target. There are at least three other countries trying to get their own probes launched first, and they play dirty.
The safest place for Bob is in space, heading away from Earth at top speed. Or so he thinks. Because the universe is full of nasties, and trespassers make them mad - very mad.
Why it's similar
Like Project Hail Mary, it features an optimistic, geeky protagonist who uses practical engineering and scientific ingenuity to solve life-or-death challenges in deep space. Both books share a lighthearted, humorous first-person voice driven by competent problem-solving.
What's different
The protagonist is a replicated digital consciousness piloting autonomous probes across the galaxy rather than a biological human on a solitary physical mission, giving the story a much wider spatial scope.