In a bit of a downer, a large mass hurtling through space colliding with the Earth would probably be a far more effective means of dispersing life than SpaceX or Blue Origin or NASA or ISRO, etc. The lack of an anthropocentric teleology is one of the things that makes Gaia both intellectually interesting and hard for people to stomach.
That's a great way of dispersing life, but a very bad way of dispersing biospheres. The Gaia Hypothesis is that the planet is a higher-order system of organisation relative to conventional living organisms, roughly analogous to how your body is is a higher-order system of organisation relative to your individual cells.
If reproducing oneself were simply a matter of dispersing your cells, then Henrietta Lacks would be the most reproductively-fit person of all time.[1] But her immortal cell-line, now living in tens of thousands of laboratories, hasn't produced any new people, which is kind of the point of reproduction. It isn't a continuation of her higher-order pattern.
Analogously, an impact-induced panspermic dispersal of radiodurans etc. might eventually seed many worlds with life, but would in no way represent a continuation of the higher-order pattern that is Gaia, and thus wouldn't be a biosphere reproducing.
I unfolded from one cell from my mother and one cell from my father. Neither -- religious views aside -- much resembled a person; particluar in physical form or scale or complexity or environmental engagement. There was data compression, so to speak.
I read Lovelock back in the late 80's so my memory may be a bit foggy, but his central point seemed to be against anthropocentrism and the hubris that humans are necessary (and by extension that phenomena like HeLa have some existential or cosmic significance). He may have been wrong and his views may not sit well with everyone, but they are reasonably honest intellectually.