If you could mount the large mailbox to the round steel post, it will be really wobbly. The best thing to do is to start over with a new post that has a side arm to mount the mailbox onto.

I hope you use your old mailbox somewhere in your yard. They are great to store your clippers and other hand gardening tools, especially if you have a little shed nearby, it give the tiny house look.

That old bracket is something cobbled together in somebody's garage. If you want to keep the post, and it's stable and not leaning, you could make a cylindrical box out of 2X pressure treated wood that slips over the post. You would cut a piece of 3/4" plywood the size of the new mail box's base, screw it on top of the wooden box, and then mount the mailbox. It would help if you also ran a bolt through the box and the steel post to keep the whole thing from rotating.

If you have any doubts about the solidity of the steel post, remove it, dig a hole, mix up a bag or two of concrete, and plant a pressure treated 4X4 in the hole; then mount the mailbox as I described above.