Yup, with one addition

>> It'll still be running some code...

until the system is degraded to the point where it crashes into either only the smallest fragments (which take tens or hundreds of millions of years to rebuild), or complete extinction

There's no particular reason that small fragments should rebuild. Multicellular organisms (beyond biofilms) were kind of a quirk of nature in the first place. (Not that I think all multicellular organisms are likely to die off – but if they did, why would they re-emerge?)

Indeed!

Yet, while I lack any deep understanding why they would re-emerge, paleontology seems to show a long history of mass extinctions down to very low levels, then re-emergence of more complex forms.

One theory that I read of a few years back posited that life, and higher forms in particular, are more efficient at increasing entropy, i.e., diffusing heat, and so are systemically favored (seen nothing on it in a few years, so no idea of its current state; if anyone recognizes it and can provide a link, thanks in advance!).

> it'll still be running some code.

This a surprisingly and pleasingly apt analogy given that DNA/RNA are indeed code being 'run' by life.