Sigh, yes there are these common and persistent myths about Scandinavian folklore based in romantic 19th century notions (and contemporary folklorists with bad methodology) where everything was basically assumed to date back to time immemorial unless someone could prove otherwise. So it's still common to see claims that Lucia, Midsummer, the Yule Goat and other stuff are all supposedly co-oped pre-Christian rituals even though those claims aren't by most historians or folklorists today.

When it comes to Lucia, it it fell on the solstice in the Julian Calendar during the Early Modern Period until the Gregorian Calendar was adopted in Scandinavia in the 1700s. The inaccuracy that was the reason for adopting a new calendar is already reason to believe it wasn't "co-opted by Christian missionaries" because Saint Lucy's day was not the solstice at the time of conversion. Additionally, Saint Lucy's day was not a feast day of any importance in medieval Scandinavia (it was a festum simplex), there was never any particular veneration of Lucy and the the celebration has nothing but the name to do with it. And if there had been a veneration of Saint Lucy it'd likely have ended with the reformation rather than starting after it, as it actually did.

No elements of Lucia date back to the Middle Ages (much less father). Unless you count the singing of Staffansvisan, which is a medieval ballad but wasn't originally associated with Lucia but rather Saint Stephen's Day (Boxing Day/the 26th). Luciatåg is a 20th century invention. The first record of a Lucia with candles in her hair is from 1764.

Now the actual origin of that Lucia figure is debated, but the debate is whether it comes from the German figure Kinken Jes (which derives ultimately from a Christ figure), as argued by the influential folklorist Carl Wilhelm von Sydow. Or from an angel figure, as argued by Nils-Arvid Bringéus.

"Lussekatt" pasteries are considered to derive from the Low German/Dutch duivekater (devil's cat) pastry/bread that Saint Nicholas supposedly distributed and the more direct translation döfvelskatt/dyfvelkatt are attested before lussekatt became the more popular term around the late 19th or early 20th century.

Popular perceptions about the winter solstice as the 'darkest day' or 'longest night' of the year, and as such a date when supernatural forces would be particularly active are likely to have played a part in the origns of the holiday. Some of those perceptions may have persisted since pre-Christian times, but that's about the largest possible extent of pre-Christian influence here. But this perception was probably not the lone cause of Lucia; as Ebbe Schön has pointed out , it was also the traditional beginning of the Christmas fast.

So to summarize the Lucia celebrations have nothing to do with Saint Lucy other than taking the name of her feast day, nor is it a continuation of pre-Christian religion in any meaningful extent. It emerged in the 17 and 18th centuries, which is easily more than 500 years after Norse peoples were completely converted.

Jan-Öyvind Swahn, Den svenska julboken, 1993

Ebbe Schön, Folktrons år, 1989

Any insight into the connection of the pastry shapes- hair, necklace, golden cats, golden cart/chariot and those same items identified to Freya?

Thank you!