filter result with $match and regular expressions inside $lookup

Question

I have this Aggregation pipeline. I am able to get the data I need with additional function like sorting and pagination. I used $lookup to add documents I need from other collections.

[ { '$match': { status: [Object] } },
  { '$lookup': { from: 'users', as: 'owner', let: { owner: "$owner" }, pipeline: [
        { $match: { $expr: { $eq: ["$$owner", "$_id"] } } },
        { $unwind: { path:"$subscriptions", preserveNullAndEmptyArrays: false} },
        { $match: { "subscriptions.active": true } },
        {
          $lookup: {
            from: "plans",
            localField: "subscriptions.plan_id",
            foreignField: "_id",
            as: "subscriptions.plans"
          }
        },
  ] }},     
  { '$unwind': { path: '$owner', preserveNullAndEmptyArrays: true } },      
  { '$sort': { location: 1 } },
  { '$skip': 0 },
  { '$limit': 20 }
]

But now, I need to filter these results with search function. I want to use regex with case insensitive to match results. How can I use regex with $match? How can I use $gte and $lte with $match for date range?

I tried using $regexMatch like,

{$match: {$regexMatch: {new RegExp(variableName, 'i')}}

but failed.

Also on $lookup for plans, how can I use $match there to filter results that have only plans from regex?