At same time this only affects a subset of Django behavior and I have used pyright with a Django codebase and it mostly worked well. The more you use very dynamic features of Django the more this matters.
One note for both is you do want to tune configuration settings. Pyright basic is fairly easy to satisfy, pyright strict is too hard for most codebases. Similarly mypy defaults are too lenient, but mypy strict is pretty hard (even mypy doesn't use strict to check itself). I roughly go for strict for both and then remove ~5 hardest rules and call that good enough. Strictest rules pretty much require all of your dependencies to be well typed/stubbed.
In general, we were very happy with the result and never looked back. Correctness and perf were both notably improved. (That pyright is also part of pylance, Microsoft’s proprietary LSP implementation for Python that plays well with VSCode, was an advantage for this particular team.)
This was about a year and a half ago so the experience may differ; both pyright and mypy + its plugins have gotten more capable and mature over time.