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Tested with 8.2 & on master.

db.a.drop()
db.a.createIndex({a:1, "b.$**":1, c: 1})
db.a.insertOne({})
db.a.explain().find({a:1, c: 1})

This produces the (sole) plan:

        indexBounds: {
          a: [ '[1, 1]' ],
          '$_path': [ '[MinKey, MaxKey]' ],
          c: [ '[MinKey, MaxKey]' ]
        }

ie. c is unconstrained.

Similarly

db.a.drop()
db.a.createIndex({a:1, 'b.$**':1, c: 1})
db.a.insertOne({})
db.a.explain().find({a:3, "b.x": {$ne: null}, c: 5})

gives a single plan with an index scan with the following bounds:

{
  a: [ '[3, 3]' ],
  '$_path': [ '[MinKey, MaxKey]' ],
  c: [ '[MinKey, MaxKey]' ]
}

where, c and $_path could both be constrained.

is related to

SERVER-129202 Wildcard indexes produce incomplete explain output due to key collision

SERVER-129049 Wildcard indices scan MinKey even when not needed

related to

SERVER-128260 Compound Wildcard Index $ne: null on indexed non-wildcard field no longer produces covered plan