Path matching is exact-match in Caddy v2 (/sonarr will only match exactly /sonarr but not /sonarr/foo), so you need to append a * to the end to match any subpath.
The HTTP 400 status is likely because sonarr is expecting the host to be something else. There must be some way to configure that.
That said, I typically recommend serving apps like Sonarr on subdomains rather than subpaths, for these reasons: