As I see it, you have three possibilities:
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Using WiFi over MQTT. As you said (and the official FAQ states), you can use it without a bridge. I think this is fine for some testing/playing around, but I would not use WiFi on a daily basis, due to the higher battery consumption.
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Using Matter over Thread with your existing Google Home as a Thread Border Router (TBR).
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I am a bit confused by your sentence “If I connect the Smart Lock Ultra to the Google Home will everything be exposed to Home Assistant? I mean will I see all states and will I be able to lock and unlock?” -
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Is your Google Home already known to HA or do you want to keep it separate?
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If it is already known, this should be very straightforward. According to the documentation (“You do not need to install this integration. The Thread integration shows up automatically when Home Assistant detects a border router.” see here), you should already have a Thread integration. Then just add the Matter integration and add the Nuki as a new Matter device. Given your background, this is the solution I would recommend at first.
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If it is not known (and should not be), this solution can be dropped by my understanding.
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Using Matter-over-Thread and your RPi as a TBR. This could either be done with the Multiprotocoll and one ZBT-1 (not recommended, but for some users it seems to work fine, so you might as well just try it). OR, you could add a second ZBT-1 and run one with ZHA and one with Thread. If you do not want to expose your Google Home to HA, I would choose this solution.
If you want some more insights, you could also have a look at a more general forum entry I did some days ago: Choosing the right Thread Border Router
But no matter how you decide, I’d love to be kept updated. Especially if you choose the Matter integration (solution 2 or 3), I would love to see what entities the lock provides.