supple valve
I'm thinking of getting Nanoleaf Essentials bulbs, but they're not supported by the Nanoleaf integration, and require the HomeKit integration.
As such, if I get the Matter version, will I need an Apple TBR in particular, or will I be able to use a much cheaper non-Apple one (say, one of the dongles)?
rich granite
You can also get a OTBR for HA add the nanoleaf Matter over Thread lights directly to HA first, then pass that light entity to apple home via the HA HomeKit Bridge. Would actually recommend the Aqara T2 bulbs over the nanoleaf ones, but the process would be the same regardless.
What you initially stated also works, get an apple TBR (HomePods or appleTV) add to apple home, then use Matter multi admin to add them to HA.