There is no build in function to achieve what you want, at least not for complicated meta queries like this. If you need to use build in functions for this, the best will be to make use of WP_Query.
To make the query faster and to skip the unwanted returned array of WP_Post properties, and because you are only interested in post count, you can use the following in your parameters in your arguments
'fields' => 'ids',
'no_found_rows' => true,
This might even be a bit faster than a custom SQL query, and the results from WP_Query is cached as well.
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