The "take with meal" instruction is common with substances requiring fat for absorption/bioavailability. Dietary fat increases vitamin D3 absorption [5].
[1] https://pubmed.ncbi.nlm.nih.gov/23665342/ The influence of vitamin D supplementation on melatonin status in patients with multiple sclerosis
[2] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4507736/ 25-Hydroxyvitamin D Concentration and Sleep Duration and Continuity: Multi-Ethnic Study of Atherosclerosis
[3] https://pubmed.ncbi.nlm.nih.gov/28652922/ The relationship between serum vitamin D levels and sleep quality in fixed day indoor field workers in the electronics manufacturing industry in Korea
[4] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5331570/ Association between Serum Vitamin D Levels and Sleep Disturbance in Hemodialysis Patients
[5] https://pubmed.ncbi.nlm.nih.gov/25441954/ Dietary fat increases vitamin D-3 absorption
More from doctors successfully treating covid with vitamins: https://youtu.be/LwlTQ52Wdro
So, broken clocks, and all that.