A chore is not a habit
Both repeat, and that is where the similarity ends. Treating them the same is why your filter is overdue and your morning routine is fine.
A habit is a behaviour you want to become automatic: the walk, the reading, the glass of water. A chore is an obligation that comes due on a schedule: the filter, the insurance, the dentist, the smoke alarm battery.
They need opposite machinery, and most systems give them the same one.
A habit needs a cue, not a date
Put a habit on a date and you have made it an appointment with yourself, which you will reschedule. Attach it to something that already happens — after coffee, before the shower — and repetition does the work.
Habits also want frequency over size. Daily and small beats weekly and ambitious, because the automatic part is built by the number of repetitions, not their weight.
A chore needs a date and nothing else
Nobody should build a habit of changing a water filter twice a year. There is nothing to automate; there is something to remember, and remembering is what a system is for.
The useful move is to record the interval rather than the next occurrence: not "filter in March" but "filter every six months, last done 14 March". The second one survives being done late, which the first does not.
Why mixing them hurts
A chore sitting in a habit tracker looks like a failed habit for five months and then becomes urgent. A habit sitting in a task list becomes a recurring overdue item, which is the fastest way to teach yourself to ignore overdue items.
Separate them once and both get easier: the habits stop being judged by a calendar, and the chores stop pretending they are character tests.