Medicare is effective retroactive to 6 months before you apply (unless you enroll when you turn 65). If you apply for Medicare 3/1/27, it will be effective retroactive to 9/1/26. I'm not sure what you are talking about by applying 3 months early, there might be a variation I am not aware of.
The point is, you need to know the Medicare effective date. That determines your HSA eligibility. If your Medicare effective date is 6/1/26, then you did correctly calculate your contribution limit for 2026, as 5/12th of $1000 plus 5/12th of $4400 (for single HDHP coverage).
That is your limit for the year, but it does not matter when during the year the contributions are made. You can even make contributions after your Medicare start date as long as the total for the year does not go over your limit. For example, you could make $187.50 per month of payroll contributions for the whole year, instead of $450 per month for 5 months then stopping after 5 months.
