This is what I and another person who's a native speaker think:
The former is the correct alternative. If it was a longer sentence, you'd probably have to add a comma after prevent, but in this case and as the sentence is, you only need one comma after but.
As a very detail-oriented person who has spent years on learning and teaching English, I cannot remember a single example of a use of but without a comma beforehand in any well-written books so far for similar sentences (not shorter/different ones), but as I'm googling now, I find out another question on ELU talking about this: Using a comma before "but", but that slightly contradicts what I've thought so far.
There are also punctuation rules on the website of University of Sussex
A joining comma must be followed by one of the connecting words and,
or, but, yet or while: The report was due last week, but it hasn't
appeared yet. The motorways in France and Spain are toll roads, while
those in Britain are free.
A gapping comma indicates that you have
decided not to repeat some words which have already occurred in the
sentence:
Jupiter is the largest planet and Pluto, the smallest.
It also continues to say:
If you're not sure about your commas, you can check them by using
these rules. Ask yourself these questions:
- Can the comma be replaced by and or or?
- Is it followed by one of the connecting words and, or, but, yet or while?
- Does it represent the absence of repetition?
- Does it form one of a pair of commas setting off an interruption which could be removed from the sentence?
It also sums it up this way:
- Use a listing comma in a list where and or or would be possible
instead.
- Use a joining comma before and, or, but, yet or while
followed by a complete sentence.
- Use a gapping comma to show that
words have been omitted instead of repeated.
- Use a pair of bracketing commas to set off a weak interruption.
It's worth mentioning that ctrl/cmd + F
ing the word but among the articles of that website (and not example sentences), I notice use of comma before but where the sentence followed by but isn't a complete sentence!
I'd say based on explanations of a joining comma and a gapping comma (as the subject [Anna] is omitted in the se, and again, discussing this with a native linguist, you better use comma before but in your sentence, but I'd like to hear more about this.