Our universe might be fined-tuned for life because there are a huge number of universes each with different laws of physics and only under a tiny set of these laws can sentient life exist and we shouldn’t be surprised to live in one of these fine-tuned universes.

I was assuming Solonomoff Induction over the full space of computable universes, which is a more principled take on fine tuning and selection effects. We should expect to find ourselves in the universe described by the simplest theory (TOE) which explains our observations.

Our universe might also be fine-tuned for the Fermi paradox, especially if advanced civilizations often create paperclip maximizers.

Paperclip maximizers are a specific absurdity with probability near zero, and I find that discussing them sucks insight out of the discussion.

Perhaps if you look at the subset of all possible laws of physics under which sentient life can exist,

This full set is infinite, complex, and irrelevant - for all we know much of this space could have life radically different than our own. It is more productive to focus on the subset of the multiverse with physics like ours - compatible with our observations. In other words - we are hardly a random observer sampled from the full set of 'sentient life'.

in a tiny subset of these you will get a Fermi paradox because, say, some quirk in the laws of physics makes interstellar travel very hard or creates a trap that destroys all civilizations before they become spacefaring.

Interstellar travel does look pretty hard, but not hard enough to prevent slow colonization. For this argument to apply to our section of the multiverse, it would need to involve new unknown physics. This is one possibility - but it seems low probability compared to other options as discussed in my post.

creates a trap that destroys all civilizations before they become spacefaring. Civilizations such as ours will constantly arise in these universes.

But then they are destroyed. I didn't describe this in my post, but from an observational selection effect, it is crucial to consider the effect of deep simulations. The universes that produce lots of deep simulations with sentient observers will tend to swamp out all other possibilities, such as those where civilizations arise but do not produce deep simulations.

The models I discussed in my post all tend to produce enormous amounts of computation applied to deep simulation - which creates enormous numbers of observers such as ourselves and vastly outweighs universes where civilizations are destroyed.

In contrast, imagine that in universes fine-tuned for life but not the Fermi paradox civilizations often create some kind of paperclip maximizer that spreads at the maximum possible speed making the development of further life impossible.

Right - we don't live in that kind of universe.