Dashes to provide parenthetical information to an item in list - example from BBC?

The technical issue here is that one kind of punctuation has overrun the other, reducing the ease of finding the elements in the list:

• the dashes mark a parenthetical statement where commas or parentheses would otherwise occur (Em-dash, The Punctuation Guide)

• commas separate three or more items of a list (Comma, The Punctuation Guide)

Without the parenthetical statement, the statement would most likely include commas like this:

[...]it is unclear whether that would come from the Duchy of Cornwall, his personal wealth, or a combination of the two.

Including the parenthetical statement, but removing no vocabulary, it looks like this:

it is unclear whether that would come from the Duchy of Cornwall - a vast portfolio of property and financial investments -, his personal wealth, or a combination of the two.

[-,], the em-dash and the comma put together, is a major infelicity. There are ways to avoid that, like leaving the parenthetical statement out, using different punctuation (commas, parentheses) to mark the parenthetical, or rephrasing. The editor chose to prioritize the em-dash distinguishing the parenthetical over the comma distinguishing the list.

It's hard to guess the reasoning of an individual editor or their style guide without more, but there is precedent for omitting a comma next to an em-dash. For an analogous example, in Chicago Manual of Style 17th edition, there's a section for what to do when em-dashes meet other punctuation (" 6.89: Em dashes with other punctuation "). It outlines two cases for omitting a comma in favor of an em-dash and none contrariwise:

If the context calls for an em dash where a comma would ordinarily separate a dependent clause from an independent clause, the comma is omitted. Likewise, if an em dash is used at the end of quoted material to indicate an interruption, the comma can be safely omitted before the words that identify the speaker (see also 6.125).