Query contacts with wix-crm-backend with custom field filter

The documentation states:
Note: When working directly with the Contact object in your code, data in extended fields must be accessed using bracket notation, like this: info.extendedFields[“{key}”]. However, when querying or sorting, extended field names are flattened with dot notation, like this: ascending(“info.extendedFields.{key}”).

So, you probably need something like this:

.eq("info.extendedFields.{sponsorUserId}", userId)