Supervisor partially putting themselves as first author even though I've done most of the work and written most of the paper

I would apply Hanlon's Razor here: "Never attribute to malice that which is adequately explained by stupidity."

This sort of mistake is easy to make when filling out journal forms: there is a lot of information to keep straight. In particular, the UI is not always designed so as to make it clear how author order will be interpreted (some forms might always want the corresponding author entered first, even if they will not be the first author). So it's not too hard to believe that someone could innocently mess it up twice.

It would also be an ineffective way for your supervisor to try to "steal" first authorship. For most journals, if the paper is accepted, every author will eventually be asked to sign a consent form agreeing to publication, and in particular, agreeing to the author ordering. You'd eventually find out and make a fuss.

But it would be fine to ask your supervisor to contact the editor and request the change, "just so that we don't forget later," or, as Azor Ahai suggests, to do it yourself. After all, your supervisor has agreed, in writing, that you are meant to be the first author.

Addition: I think perhaps the author list inputted in the online fields may be used for citations but the paper itself will have me as first author. So perhaps my supervisor wants their name to be that cited?

No, it doesn't work like that. The journal is going to want one and only one author ordering, to be used both on the paper itself and for all metadata and citations. They should always match. If there is a discrepancy between the manuscript and the online fields, the journal will insist that the authors resolve it before publication.

The first answer to this question suggests that this might be incompetence rather than malevolence. A second (and to me more likely) possibility is that it's neither malevolence nor incompetence, but simply bureaucracy.

Your description is confusing and it seems possible that you misunderstand what's happened here. With many journal submissions, there's a series of boxes where you enter authors' names and information. These boxes are not necessarily related to author order! You can enter names in any order you want and it's completely irrelevant to the actual published author order. Often the first box is for the corresponding author, who is not necessarily the first author.

From your description, it sounds like this has happened. If so, probably the reason your advisor is so casual about this is that it's completely trivial; it has no bearing on your concern. The author order is the order in the manuscript and you're worrying about something that's not an issue.

It's also possible that the advisor thinks this has happened but the order is relevant, but from the way you've described it that doesn't seem to be the case.

A bigger issue, to me, seems to be your relationship with your advisor. Even though your advisor promised you first authorship, reiterated the promise, and assured you that the issue would be corrected, you've leaped to the conclusion that they are trying to "steal" your authorship. If you mistrust your advisor to this extent, is this a healthy situation? Has the advisor done anything to justify this immediate and very harsh reaction, or is this a case of paranoia? It seems to me that the answer, either way, is likely to have a much bigger effect on your career than an apparent minor misunderstanding.