After posting this question, I found there's some discussion on it.
The gemarra Horayos 8b says the following
(במדבר טו, כג) למן היום אשר צוה ה' והלאה לדורותיכם איזו היא מצוה שהיא נאמרה בתחלה הוי אומר זו עבודת כוכבים
“All that the Lord has commanded you by the hand of Moses, from the day that the Lord commanded and onward throughout your generations” (Numbers 15:23). Which is the mitzva that was stated at the beginning of all the mitzvot? You must say: This is idol worship.
The Rashbatz in Sefer HaTashbetz I § 139 points out that this sounds like the opinion of the Bahag, that that "I am Hashem your G-d" isn't a mitzvah. The Rambam et. al say that the first of the Ten Commandments is "I am Hashem your G-d", and the second one is against idol worship. Since the gemarra is saying that the first mitzvah was against idol worship, and not "I am Hashem", it must not be counted.
He deflects this proof to the Bahag by suggesting that "I am Hashem" and "Have no other gods before Me" were one statement (see there, where he retracts from this). Thus, both of them comprise the First Commandment. The statement about not making idols would then be the Second Commandment.
Rav Yerucham Fischel Perla likes this suggestion, and brings the above quoted Sifrei as a support. Although he brings many sources that seem to disagree, he is fine to say it's a machlokes, a dispute.
He seems to finish off that this Sifrei is of the opinion like the Rashbatz's suggestion, that they really are all part of the First Commandment.