updateOne based on condition

Question

await products.updateOne(
        {
          $and: [
            { name: { $eq: name } },
            { $expr: { $lt: ["$remaining", "$capacity"] } },
          ],
        },
        { $inc: { remaining: 1 } },
        { returnOriginal: false }
      );

Instead of having the condition in the query like so { $expr: { $lt: ["$remaining", "$capacity"] } }, is there a way to include this condition in the update argument?

The reason for this is so that I want the returned matchCount to return 1 if the name is matched.