… I don’t think that it ever was an official or infallible teaching that a dragon would have to represent the devil, but that is how it has been portrayed, at least with the icons of St. Michael. That has been changed now and we do not even have the prayer to St. Michael the Archangel at the end of the New Mass, even though this prayer was standard at the end of Mass before Vatican II. So it is a change. Now we see dragons parading in Church and we are told that it is good luck if we can touch the dragon. This is a rather serious change from the outlook before, when this would have been unthinkable.
Although I agree that the Catholic church has reversed itself in the past and continues to morph itself, I think the dragon issue is a misfire.
This is strictly a cultural expression.
There is nothing wrong with using dragons as a personification of evil, that happens to be a common theme in Europe (in times past). If the church is going to be always Euro-centric this is not a problem.
The east Asians (I am thinking particularly of the Chinese) have always seen dragons in a better light, so artistically it doesn’t work. Likewise equating Satan with a dragon before a Chinese audience would be teaching the exact opposite of what one intends, Satan would be subconsciously glorified.
In historical fact, dragons were also taken represent the power of the emperor, and the phoenix (actually, it looks a bit like a peacock to me) is the power of the queen. On official buildings and monuments two dragons are sometimes interposed with a globe or ball in play between them. Most emperors in recent dynasties used nine dragons as a decorative motif on everything in the household, so if you find an old vase from China with nine dragons on it get it appraised

.
None of this is theological, it’s just an aspect of culture one might appropriate to illustrate a point. The church itself is not wedded to the concept of evil dangerous dragons like Smaug.
What disturbs me about what you have written is that you say " …and we are told that it is good luck if we can touch the dragon". If you are correct about this, or have witnessed it in the church yourself I would say that it is an abuse. The church does not teach that touching
anything will bring one good luck.
It’s simply not Christian.
Is it written down anywhere as an infallible statement that it is wrong to pray to St. Michael the Archangel at the end of every Mass? I don;t see where it is. But the de facto truth is that this prayer is no longer said at the end of the New Mass.
I remember that. I know that it refers to Satan as a serpent and a dragon (I suppose that these were intended to be insults, but that just shows us how much Pope Leo was bound to his own culture and unaware that his own Asian Catholic subjects would not appreciate the reference), but the shorter version I actually remember saying does not use the terms.
However I think (others may correct me) that this particular prayer was not actually part of the Mass. It was said
after the Mass and was not that long a practice (perhaps 100 years? I don’t know … ).
Anyway, we all have to get to the parking lot and pull out before the people coming for the next Mass choke up the exits! We can say it in the car!

lol
Honestly, I like the prayer and approve of the thinking behind it. It is not wrong to pray at any time.
Sancte Michael Archangele, defende nos in proelio;
contra nequitiam et insidias diaboli esto praesidium.
Imperet illi Deus, supplices deprecamur:
tuque, Princeps militiae Caelestis, satanam aliosque spiritus malignos, qui ad perditionem animarum pervagantur in mundo, divina virtute in infernum detrude.
Amen.