count (DISTINCT field) OVER ()

I would like to implement the equivalent of "count (DISTINCT field) OVER
()":

SELECT
id, name, similarity(name, 'Tooneyvara') as delta,
count (id) OVER() AS cnt
FROM vtown
WHERE
similarity(name, 'Tooneyvara') > 0.1
ORDER BY delta DESC

produces result:
1787 Toomyvara 0.5 4
1787 Toomevara 0.4 4
1700 Ardcroney 0.105 4
1788 Townsfield 0.1 4

What I would like is a "3" in the cnt column (ignoring id duplicates).

How can I achieve this?

The best I can come up with is:

SELECT id, name,delta, count (*) OVER()
FROM (
SELECT DISTINCT ON (id)
id, name, similarity(name, 'Tooneyvara') as delta
FROM vtown
WHERE
similarity(name, 'Tooneyvara') > 0.1
ORDER BY id, delta DESC
) AS x
ORDER by delta DESC

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Best Regards,
Tarlika Elisabeth Schmitz