No , iDVD cannot burn Blu-ray.( or AVCHD, see below).
You use FCPX.
Instead of File>Share > Master File it is File>Share >Blu-ray.
The Blu-ray destination does not appear by default if you have not used it before.
To add it to your set of destinations and to the Share menu, choose File > Share > Add Destination, then double-click the Blu-ray destination.
The following is a link to the FCPX help guide
https://support.apple.com/en-gb/guide/final-cut-pro/ver6c4cb86b5/mac
You will see that it mentions Blu-ray and AVCHD discs.
Blu-ray is on Blu-ray disc (BD) and AVCHD is on DVD disc.
Blu-ray needs Blu-ray burner plus BD disc to burn and Blu-ray player to play.
AVCHD needs DVD burner plus DVD disc to burn( or Blu-ray burner plus DVD disc) and Blu-ray player to play.
It can be confusing, you might want to Google for more info'.
AVCHD is similar to Blu-ray but not such high bit rate, so quality not quite as good, but better than standard DVD.
Amount of time on AVCHD is limited to about 20 minutes due to capacity of DVD disc.
You might want to try the AVCHD option first as DVD is cheaper than BD, especially if your video is 20 minutes or so.
I am pretty sure that the disk image option is for Blu-ray only and not AVCHD so if you are going for AVCHD then you will have to select your optical device ( burner) as the Output Device .
If you are going for Blu-ray then you can select Hard Drive as the output device for disk image or optical device (Blu-ray burner ) for direct to BD disc.( section 5 in the link).