Chanukah Candle Lighting Blessings Order

Hello Rabbi,
From what I know, there are several scenarios in which the order of precedence in the blessings is determined by considerations such as "moving on to their fulfillment" or a pause between matters – for example, prioritizing the blessing of the Creator of the Fruit of the Tree, prioritizing sitting in the Sukkah for the blessing of the Exorcist, and perhaps also prioritizing the blessing of the Exorcist for lighting a candle. Despite this, I have not found anyone who addresses the issue in relation to the blessing of the Hanukkah candle (and similarly, reading the Megillah, the shofar, and perhaps a number of other mitzvot that I forget) – seemingly it would be better to recite the blessing of the One who performed miracles, the blessing of the One who performed them, then light a Hanukkah candle and move straight to lighting it.
I would be very grateful to the rabbi if he could sort out the various reasons, the differences between the above issues, and whether there is any relevance to the Chanukah candle blessing order.
Happy Hanukkah!