TL;DR: it's less than 1/4 point ABV per volume of CO2 added at bottling time. As @rob said, that is negligible for my personal level of homebrew measurement precision.
To provide some math to back up @dmtaylor's answer, here's what I found:
From this thread https://www.homebrewersassociation.org/forum/index.php?topic=5882.0
100 grams of sugar in enough water to make 1 liter total gives you a solution that is 10% sugar. This corresponds to 10 brix, which is ~1.040.
From this article https://byo.com/article/master-the-action-carbonation/#:~:text=The%20amount%20of%20CO2,Temperature%20and%20Pressure%20(STP), I computed that 1 volume of CO2 is 15.25 g sugar per gallon, which divided into 3.8 L, is approximately 4 g sugar per L of beer. Assuming that 4 g has negligible volume displacement, that gives me 0.4oBx ~= 2 gravity points (1.002). At 100% Apparent Attenuation, that would give me about 0.25% ABV per volume of CO2, or 0.5% ABV for a typical (for me) 2 volumes CO2.
Combine that with this article about apparent attenuation https://beerandbrewing.com/everything-you-need-to-know-about-attenuation/ and typical attenuation around 70-80%, should give me <= 80% * 2 GP = 1.6 GP of fermentation.
According to this calculator https://www.brewersfriend.com/abv-calculator/ 1.002 -> 1.0004 gravity drop, I get up to 0.2% ABV per volume CO2
Since that validates what @dmtaylor said, I'll consider that good enough math for now. If somebody can do the math from moles ethanol to points ABV, I'll be very happy.