Beatrice's Titles

As a witch, Beatrice holds two titles: "Golden" and "Endless".
These originally came from separate Magical Compendiums, so it can be said she wields the power of two compendiums.

The title of Endless Witch has its foundation in "Endless Creation" and is the root of her unmatched, endless magical power.
The title of Golden Witch has its foundation in "the Realization of Magic", a magical power that can materialize imaginary precious metals, providing the miracle of manifestation to all less tangible forms of magic.

These two titles were refined even further with Mariage Sorcière leading to their sublimation into the compendium known as "Endless Realization".

In that sense, she technically shouldn't be referred as either the Endless Witch or the Golden Witch, but by a new title that is a fusion of the two.

Beatrice's Titles

Beatrice's Titles (golden and endless) are passed down through different unrelated means. The former involves solving The Portrait Epitaph while the latter is a long

During the coronation of Evato, Beatrice confirms she is inheriting both titles.

According to Maria's diary the main criterion for coronating a golden witch seems to be solving the epitaph.

But unless we completely write off the tips as magical nonsense, we know the sequence of endless witches is recommendation based and it pre-dates Virgilia by some generations, hinting at a different real world parallel.

The Golden Witch is Kinzo's version of Beatrice

This is the Beatrice made up by Kinzo to convince everyone that he possessed 10 tons of gold. Even to this day the modern incarnation of beatrice is supporting this claim and identifying with the image and narrative Kinzo has created because it's a valuable addition to her own narrative (Endless Realization).

Leads:

It's the title inherited by solving The Portrait Epitaph.
The description of golden magic from Beatrice's Titles literally says it can "materialize imaginary precious metals".

Endless magic is a folk tale

The origin of the endless magic narrative is a kind of folklore passed down in Kumasawa's family. It pre-dates Kinzo's golden witch narrative and it could have been a source of inspiration for him, or maybe the two concepts were separate until they were merged by Sayo and X Beatrice, who were raised around both of them.

Maria has contributed her imagination and occult hyper fixation, but she didn't come up with the whole thing like we initially theorized. Maybe "gaining endless power" means entering the public consciousness, and the Rokkenjima case was instrumental for that to happen with Beatrice.

Leads:

The magical lore fluff in Regarding the Succession of Witches hints at a long lineage of endless witches, but nothing of the sort exists about the golden witch.
Virgilia, aka. Kumasawa is the previous endless witch, but seemingly not a golden witch.