I also use Apple TV + HomePods mini for TBRs because I already had them, and they work well. While these need cloud access for some functions (e.g. voice control, streaming), they don’t require it for Thread routing.
There are other, cheaper options for TBRs. You can get the GL.iNet GL-S20 for under $50 right now, which has PoE, or the (wifi-only) barebones board it uses for around $20, both of which are standalone OTBR devices. Popular dongles like ZBT-1 and SZLB-xxx go for around $30-45 but require the OTBR container/add-on software running on a server (e.g. HAOS). As a “bare minimum” I got a esp32-h2 dev board for $5 and flashed it with “Thread RCP” firmware, which functions the same as a dongle.
Since TBRs are just network routers, there is very little for HA to participate in their configuration or control, so basically any vendor “works” with HA, while OTBR-based routers with a REST API endpoint can be lightly configured by a HA integration.
For all routers you need to either (a) commission new devices to the native (Apple/Google/Amazon) Matter fabric first, then share it to HA, or (b) sync the credentials to the HA mobile companion app (iCloud keychain / Google Play Service) on your phone to commission devices directly to the HA Matter fabric. The end result is the same. There is an option for server-only commissioning for advanced users.