Petitions are not Prayers of Thanksgiving
Prayer of Thanksgiving is a very important aspect of Christian prayer. Eucharist is Thanksgiving. The Eucharist is to be the summit and source of all Christian life.
The Prayer of the Faithful is a prayer of petition, a prayer of intercession, a distinctive form of prayer, a very legitimate form of prayer a form of prayer that comes naturally, one might say.
The petitions or intentions that are voiced in the Prayer of the Faithful are prayers of petition.
As far as the Prayer of the Faithful in the Liturgy is concerned, it is inappropriate to include petitions of thanksgiving into the intercession pattern.
We sometimes hear in the Prayer of the Faithful: We thank you Father for X, Y and Z. Lord, hear us. Such a statement is out of place in the Prayer of the Faithful.
Specific statements of thanksgiving can appropriately be included in the introduction to the Lay Led Liturgy or prior to the Prayer of Thanksgiving, or perhaps included in a reflection after Communion, if there is Communion at the Lay Led Liturgy.